ReturnIn this loan, each total payment is different, with each succeeding payment -less than the preceding payment. Each payment is the total of the constant -amount to the principal plus the interest for the period. The constant payment -to the principal is computed as: - -
- C = -PV / N - --Where PV is the loan amount to be repaid in N payments (periods). Thus the -principal after the first payment is: - -
- PV[1] = PV[0] + C = PV + C -- -after the second payment, the principal is: - -
- PV[2] = PV[1] + C = PV[0] + 2C -- -In general, the remaining principal after n payments is: - -
- PV[n] = PV[0] + nC = PV + nC -- -If the effective interest per payment period is i, then the interest for the -first payment is: - -
- I[1] = -i*PV[0] -- -and for the second: - -
- I[2] = -i * PV[1] -- -and in general, for the n'th payment the interest is: - -
- I[n] = -i * PV[n-1] - = -i * (PV + (n - 1)C) -- -The total payment for any period, n, is: - -
- P[n] = C + I[n] - = C - i * (PV + (n - 1)C) - = C(1 + i) - i * (PV + nC) -- -The total interest paid to period n is: - -
- T[n] = I[1] + I[2] + I[3] + ... + I[n] - T[n] = sum(j = 1 to n: I[j]) - T[n] = sum(j = 1 to n: -i * (PV + (j-1)C)) - T[n] = sum(j=1 to n: -i*PV) + sum(j=1 to n: iC) + sum(j=1 to n: -iCj) - T[n] = -i*n*PV + i*n*C - i*C*sum(j=1 to n:j) - sum(j=1 to n:j) = n(n+1)/2 - T[n] = -i*n*(PV + C) - i*C*n(n+1)/2 - T[n] = -i*n*(PV + (C*(n - 1)/2)) -- -Note: substituting for C = -PV/N, in the equations for PV[n], I[n], P[n], and T[n] -would give the following equations: - -
- PV[n] = PV*(1 - n/N) - I[n] = -i*PV*(1 + N - n)/N - P[n] = -i*PV*(2 + N - n)/N - T[n] = -i*n*PV*(2*N - n + 1)/(2*N) -- -Using these equations for the calculations would eliminate the dependence -on C, but only if C is always defined as above and would eliminate the -possibility of another value for C. If the value of C was less than -PV/N -then a balloon payment would be due at the final payment and this is a possible -alternative for some people. diff --git a/libgnucash/doc/dia/components.dia b/libgnucash/doc/dia/components.dia deleted file mode 100644 index 6fec466415..0000000000 Binary files a/libgnucash/doc/dia/components.dia and /dev/null differ diff --git a/libgnucash/doc/dia/structures-alt.dia b/libgnucash/doc/dia/structures-alt.dia deleted file mode 100644 index 926ead4870..0000000000 Binary files a/libgnucash/doc/dia/structures-alt.dia and /dev/null differ diff --git a/libgnucash/doc/dia/structures.dia b/libgnucash/doc/dia/structures.dia deleted file mode 100644 index 26609e87d6..0000000000 Binary files a/libgnucash/doc/dia/structures.dia and /dev/null differ diff --git a/libgnucash/doc/finderv.html b/libgnucash/doc/finderv.html deleted file mode 100644 index f370d15eb2..0000000000 --- a/libgnucash/doc/finderv.html +++ /dev/null @@ -1,337 +0,0 @@ - -
- -Financial Equations Documentation - - - -Return -
-
-
The financial equation is derived in the following manner: - -
Start with the basic equation to find the balance or Present Value, PV[1], after -one payment period. Note PV[1] is the Present Value after one payment and PV[0] -is the initial Present Value. PV[0] will be shortened to just PV. - -
The interest due at the end of the first payment period is the original present value, -PV, times the interest rate for the payment period plus the periodic payment times the -interest rate for beginning of period payments: - -
ID[1] = PV * i + X * PMT * i = (PV + X * PMT) * i - -
The Present Value after one payment is the original Present Value with the periodic -payment, PMT, and interest due, ID[1], added: - -
- PV[1] = PV + (PMT + ID[1]) - PV[1] = PV + (PMT + (PV + X * PMT) * i) - PV[1] = PV * (1 + i) + PMT * (1 + Xi) -- -
This equation works for all of the cash flow diagrams shown previously. The Present Value, -money received or paid, is modified by a payment made at the beginning of a payment -period and multiplied by the effective interest rate to compute the interest -due during the payment period. The interest due is then added to the payment -to obtain the amount to be added to the Present Value to compute the new Present Value. - -
For diagram 1): PV < 0, PMT == 0, PV[1] < 0
-
For diagram 2): PV == 0, PMT < 0, PV[1] < 0
-
For Diagram 3): PV > 0, PMT < 0, PV[1] >= 0 or PV[1] <= 0
-
For Diagram 4): PV < 0, PMT > 0, PV[1] <= 0 or PV[1] >= 0
-
-
X may be 0 or 1 for any diagram. - -
For the standard loan, PV is the money borrowed, PMT is the periodic payment to repay -the loan, i is the effective interest rate agreed upon and FV is the residual loan amount -after the agreed upon number of periodic payment periods. If the loan is fully paid off -by the periodic payments, FV is zero, 0. If the loan is not completely paid off after the -agreed upon number of payments, a balloon payment is necessary to completely pay off the loan. -FV is then the amount of the needed balloon payment. For a loan in which the borrower pays -only enough to repay the interest due during a payment period, interest only loan, the -balloon payment is equal to the negative of PV. - -
To calculate the Present Value after the second payment period, the above calculation -is applied iteratively to PV[1] to obtain PV[2]. In fact to calculate the Present Value -after any payment period, PV[n], the above equation is applied iteratively to PV[n-1] -as shown below. - -
- PV[2] = PV[1] + (PMT + (PV[1] + X * PMT) * i) - = PV[1] * (1 + i) + PMT * (1 + iX) - = (PV * (1 + i) + PMT * (1 + iX)) * (1 + i) + PMT * (1 + iX) - = PV * (1 + i)^2 + PMT * (1 + iX) * (1 + i) - + PMT * (1 + iX) -- -
Similarly, PV[3] is computed from PV[2] as: - -
- PV[3] = PV[2] + (PMT + (PV[2] + X * PMT) * i) - = PV[2] * (1 + i) + PMT * (1 + iX) - = (PV * (1 + i)^2 + PMT * (1 + iX) * (1 + i) - + PMT * (1+ iX)) * (1 + i) - + PMT * (1+ iX) - = PV * (1 + i)^3 + PMT * (1 + iX) * (1 + i)^2 - + PMT * (1 + iX) * (1 + i) - + PMT * (1 + iX) -- -
And for the n'th payment, PV[n] is computed from PV[n-1] as: - -
- PV[n] = PV[n-1] + (PMT + (PV[n-1] + X * PMT) * i) - PV[n] = PV * (1 + i)^n + PMT * (1 + iX) * (1 + i)^(n-1) - + PMT * (1 + iX) * (1 + i)^(n-2) + - . - . - . - + PMT * (1 + iX) * (1 + i) - + PMT * (1 + iX) - PV[n] = PV * (1 + i)^n + PMT * (1 + iX) * [(1 + i)^(n-1) + ... + (1 + i) + 1] -- -
The formula for PV[n] can be proven using mathematical induction.
-
-
-Basic Financial Equation
-
As shown above, the basic financial transaction equation is simply: - -
- PV[n] = PV[n-1] + (PMT + (PV[n-1] + X * PMT) * i) - = PV[n-1] * (1 + i) + PMT * (1 + iX) - for: n >= 1 -- -
relating the Present Value after n payments, PV[n] to the previous Present Value, PV[n-1]. - - - -
The sum of the finite series: - -
1 + k + (k^2) + (k^3) + ... + (k^n) = (1-k^(n+1))/(1-k) - -
as can be seen by the following. Let S(n) be the series sum. Then - -
S(n) - k * S(n) = 1 - k^(n+1) - -
and solving for S(n): - -
S(n) = (1-k^(n+1))/(1-k) = 1 + k + (k^2) + (k^3) + ... + (k^n) - - -
Using this in the equation above for PV[n], we have: - -
- PV[n] = PV * (1 + i)^n + PMT * (1 + iX) * [(1 + i)^(n-1) + ... + (1 + i) + 1] - = PV * (1 + i)^n + PMT * (1 + iX) * [1 - (1 + i)^n]/[1 - (1 + i)] - = PV * (1 + i)^n + PMT * (1 + iX) * [1 - (1 + i)^n]/[-i] - = PV * (1 + i)^n + PMT * (1 + iX) * [(1 + i)^n - 1]/i -- -
or: - -
- PV * (1 + i)^n + PMT * [(1 + i)^n - 1]/i - PV[n] = 0 -- -
If after n payments, the remaining balance is repaid as a lump sum, the lump sum -is known as the Future Value, FV[n]. Since FV[n] is negative if paid and positive -if received, FV[n] is the negative of PV[n]. - -
Setting: FV[n] = -PV[n] - -
Since n is assumed to be the last payment, FV[n] will be shortened to simply -FV for the last payment period. - -
- PV*(1 + i)^n + PMT*(1 + iX)*[(1 + i)^n - 1]/i + FV = 0 -- -
Up to this point, we have said nothing about the value of PMT. PMT can be any value mutually -agreed upon by the lender and the borrower. From the equation for PV[1]: - -
- PV[1] = PV + (PMT + (PV + X * PMT) * i), -- -
Several things can be said about PMT. - -
The payment is exactly equal to the interest due and PV[1] = PV. In this case, the borrower -must make larger future payments to reduce the balance due, or make a single payment, after -some agreed upon number of payments, with PMT = -PV to completely pay off the loan. This is -an interest only payment with a balloon payment at the end. - -
The payment is insufficient to cover even the interest charged and the balance due grows - -
The payment is sufficient to cover the interest charged with a residual amount to be -applied to reduce the balance due. The larger the residual amount, the faster the loan is -repaid. For most mortgages or other loans made today, the lender and borrower agree upon -a certain number of repayment periods and the interest to be charged per payment period. -The interest may be multiplied by 12 and stated as an annual interest rate. Then the -lender and borrower want to compute a periodic payment, PMT, which will reduce the balance -due to zero after the agreed upon number of payments have been made. If N is the agreed -upon number of periodic payments, then we want to use: - -
- PV * (1 + i)^N + PMT*(1 +iX)*[(1 + i)^N - 1]/i + FV = 0 -- -
with FV = 0 to compute PMT: - -
- PMT = -[PV * i * (1 + i)^(N - X)]/[(1 + i)^N - 1] -- -
The value of PMT computed will reduce the balance due to zero after N periodic payments. -Note that this is strictly true only if PMT is not rounded to the nearest cent as is the -usual case since it is hard to pay fractional cents. Rounding PMT to the nearest cent has -an effect on the FV after N payments. If PMT is rounded up, then the final Nth payment -will be smaller than PMT since the periodic PMTs have paid down the principal faster than -the exact solution. If PMT is rounded down, then the final Nth payment will be larger than -the periodic PMTs since the periodic PMTs have paid down the principal slower than the -exact solution. -
With a simple alegebraic re-arrangement, The financial Equation becomes: - -
- 2) [PV + PMT*(1 + iX)/i][(1 + i)^n - 1] + PV + FV = 0 -- -
or - -
- 3) (PV + C)*A + PV + FV = 0 -- -
where: -
- 4) A = (1 + i)^n - 1 - - 5) B = (1 + iX)/i - - 6) C = PMT*B -- -
The form of equation 3) simplifies the calculation procedure for all five -variables, which are readily solved as follows: - -
- 7) n = ln[(C - FV)/(C + PV)]/ln((1 + i) - - 8) PV = -[FV + A*C]/(A + 1) - - 9) PMT = -[FV + PV*(A + 1)]/[A*B] - - 10) FV = -[PV + A*(PV + C)] -- -
Equations 4), 5) and 6) are computed by the functions in the "fin.exp" utility:
-
-
_A
-
_B
-
_C
-
-
respectively. Equations 7), 8), 9) and 10) are computed by functions:
-
-
_N
-
_PV
-
_PMT
-
_FV
-
-
respectively. - -
The solution for interest is broken into two cases: - -
Equation 3) can be solved exactly for i: - -
- i = [FV/PV]^(1/n) - 1 -- -
Since equation 3) cannot be solved explicitly for i in this case, an -iterative technique must be employed. Newton's method, using exact -expressions for the function of i and its derivative, are employed. The -expressions are: - -
- 12) i[k+1] = i[k] - f(i[k])/f'(i[k]) - where: i[k+1] == (k+1)st iteration of i - i[k] == kth iteration of i - and: - - 13) f(i) = A*(PV+C) + PV + FV - - 14) f'(i) = n*D*(PV+C) - (A*C)/i - - 15) D = (1 + i)^(n-1) = (A+1)/(1+i) -- -
To start the iterative solution for i, an initial guess must be made -for the value of i. The closer this guess is to the actual value, -the fewer iterations will have to be made, and the greater the -probability that the required solution will be obtained. The initial -guess for i is obtained as follows: - -
- | n*PMT + PV + FV | - 16) i[0] = | ----------------| - | n*PV | - - = abs[(n*PMT + PV + FV)/(n*PV)] -- -
- | FV - n*PMT | - 17) i[0] = |---------------------------| - | 3*[PMT*(n-1)^2 + PV - FV] | - - = abs[(FV-n*PMT)/(3*(PMT*(n-1)^2+PV-FV))] -- - -
- | FV + n*PMT | - 18) i[0] = |---------------------------| - | 3*[PMT*(n-1)^2 + PV - FV] | - - = abs[(FV+n*PMT)/(3*(PMT*(n-1)^2+PV-FV))] -- -
Return
-
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-
-
-
-
-Financial Calculator - - - - -
This is a complete financial computation utility to solve for the five -standard financial values: n, %i, PV, PMT and FV -
In addition, four additional parameters may be specified: -
When an amortization schedule is desired, the financial transaction Effective Date, ED, -and Initial Payment Date, IP, must also be entered. - -
Canadian and European style mortgages can be handled in a simple, -straight-forward manner. Standard financial sign conventions are used: - -
"Money paid out is Negative, Money received is Positive" -
If you borrow money, you can expect to pay rent or interest for its use;
-conversely you expect to receive rent interest on money you loan or invest.
-When you rent property, equipment, etc., rental payments are normal; this
-is also true when renting or borrowing money. Therefore, money is
-considered to have a "time value". Money available now, has a greater value
-than money available at some future date because of its rental value or the
-interest that it can produce during the intervening period.
-
-
-Simple Interest
-
If you loaned $800 to a friend with an agreement that at the end of one
-year he would would repay you $896, the "time value" you placed on your
-$800 (principal) was $96 (interest) for the one year period (term) of the
-loan. This relationship of principal, interest, and time (term) is most
-frequently expressed as an Annual Percentage Rate (APR). In this case the
-APR was 12.0% [(96/800)*100]. This example illustrates the four basic
-factors involved in a simple interest case. The time period (one year),
-rate (12.0% APR), present value of the principal ($800) and the future
-value of the principal including interest ($896).
-
-
-Compound Interest
-
In many cases the interest charge is computed periodically during the term
-of the agreement. For example, money left in a savings account earns
-interest that is periodically added to the principal and in turn earns
-additional interest during succeeding periods. The accumulation of interest
-during the investment period represents compound interest. If the loan
-agreement you made with your friend had specified a "compound interest
-rate" of 12% (compounded monthly) the $800 principal would have earned
-$101.46 interest for the one year period. The value of the original $800
-would be increased by 1% the first month to $808 which in turn would be
-increased by 1% to 816.08 the second month, reaching a future value of
-$901.46 after the twelfth iteration. The monthly compounding of the nominal
-annual rate (NAR) of 12% produces an effective Annual Percentage Rate (APR)
-of 12.683% [(101.46/800)*100]. Interest may be compounded at any regular
-interval; annually, semiannually, monthly, weekly, daily, even continuously
-(a specification in some financial models).
-
-
-Periodic Payments
-
When money is loaned for longer periods of time, it is customary for the
-agreement to require the borrower to make periodic payments to the lender
-during the term of the loan. The payments may be only large enough to repay
-the interest, with the principal due at the end of the loan period (an
-interest only loan), or large enough to fully repay both the interest and
-principal during the term of the loan (a fully amoritized loan). Many loans
-fall somewhere between, with payments that do not fully cover repayment of
-both the principal and interest. These loans require a larger final payment
-(balloon) to complete their amortization. Payments may occur at the
-beginning or end of a payment period. If you and your friend had agreed on
-monthly repayment of the $800 loan at 12% NAR compounded monthly, twelve
-payments of $71.08 for a total of $852.96 would be required to amortize the
-loan. The $101.46 interest from the annual plan is more than the $52.96
-under the monthly plan because under the monthly plan your friend would not
-have had the use of $800 for a full year.
-
-
-Financial Transactions
-
The above paragraphs introduce the basic factors that govern most
-financial transactions; the time period, interest rate, present value,
-payments and the future value. In addition, certain conventions must be
-adhered to: the interest rate must be relative to the compounding frequency
-and payment periods, and the term must be expressed as the total number of
-payments (or compounding periods if there are no payments). Loans, leases,
-mortgages, annuities, savings plans, appreciation, and compound growth are
-among the many financial problems that can be defined in these terms. Some
-transactions do not involve payments, but all of the other factors play a
-part in "time value of money" transactions. When any one of the five (four
-- if no payments are involved) factors is unknown, it can be derived from
-formulas using the known factors.
-
-
-Standard Financial Conventions
-
The Standard Financial Conventions are: - -
If payments are a part of the transaction, the number of payments must -equal the number of periods (n). - -
Payments may be represented as occurring at the end or beginning of the -periods. - -
Diagram to visualize the positive and negative cash flows (cash flow -diagrams): - -
Amounts shown above the line are positive, received, and amounts shown below the -line are negative, paid out. - -
- A FV* - 1 2 3 4 . . . . . . . . . n | - Period +---+---+---+---+---+---+---+---+---+---+---+---+---+---+ - | - V - PV -- - - - -
- PV = 0 A - | - Period +---+---+---+---+---+---+---+---+---+---+---+---+---+---+ - | 1 | 2 | 3 | 4 | . | . | . | . | . | . | . | . | . | n - V V V V V V V V V V V V V V - PMT PMT PMT PMT PMT PMT PMT PMT PMT PMT PMT PMT PMT PMT -- - - - -
- PV ^ - | FV=0 - Period +---+---+---+---+---+---+---+---+---+---+---+---+---+---+ - 1 | 2 | 3 | 4 | . | . | . | . | . | . | . | . | . | n | - V V V V V V V V V V V V V V - PMT PMT PMT PMT PMT PMT PMT PMT PMT PMT PMT PMT PMT PMT -- - - -
- A FV* - PMT PMT PMT PMT PMT PMT PMT PMT PMT PMT PMT PMT PMT | + - A A A A A A A A A A A A A A PMT - 1 | 2 | 3 | 4 | . | . | . | . | . | . | . | . | . | n | - Period +---+---+---+---+---+---+---+---+---+---+---+---+---+---+ - | - V - PV -- - - -
Before discussing the financial equation, we will discuss interest. Most
-financial transactions utilize a nominal interest rate, NAR, i.e., the interest
-rate per year. The NAR must be converted to the interest rate per payment
-period and the compounding accounted for before it can be used in computing
-an interest payment. After this conversion process, the interest used is the
-effective interest rate, EIR. In converting NAR to EIR, there are two concepts
-to discuss first, the Compounding Frequency and the Payment Frequency and
-whether the interest is compounded in discrete intervals or continuously.
-
-
-Compounding Frequency
-
The compounding Frequency, CF, is simply the number of times per year, the
-monies in the financial transaction are compounded. In the U.S., monies
-are usually compounded daily on bank deposits, and monthly on loans. Sometimes
-long term deposits are compounded quarterly or weekly.
-
-
-Payment Frequency
-
The Payment Frequency, PF, is simply how often during a year payments are
-made in the transaction. Payments are usually scheduled on a regular basis
-and can be made at the beginning or end of the payment period. If made at
-the beginning of the payment period, interest must be applied to the payment
-as well as any previous money paid or money still owed.
-
-
-Normal CF/PF Values
-
Normal values for CF and PF are: -
The Compounding Frequency per year, CF, need not be identical to the -Payment Frequency per year, PF. Also, -Interest may be compounded in either discrete intervals or continuously -compounded and payments may be made at the beginning of the payment period or at the -end of the payment period. - -
CF and PF are defaulted to 12. The default is for discrete interest intervals -and payments are defaulted to the end of the payment period. - -
When a solution for n, PV, PMT or FV is required, the nominal interest
-rate, i, must first be converted to the effective interest rate per payment
-period. This rate, ieff, is then used to compute the selected variable. To
-convert i to ieff, the following expressions are used:
-
-
-NAR to EIR for Discrete Interest Periods
-
To convert NAR to EIR for discrete interest periods: - -
ieff = (1 + i/CF)^(CF/PF) - 1
-
-
-NAR to EIR for Continuous Compounding
-
to convert NAR to EIR for Continuous Compounding: - -
ieff = e^(i/PF) - 1 = exp(i/PF) - 1 - -
When interest is computed, the computation produces the effective interest
-rate, ieff. This value must then be converted to the nominal interest rate.
-Function _I in the "fin.exp" utility returns the nominal interest
-rate NOT the effective interest rate. ieff is converted to i using the following expressions:
-
-
-EIR to NAR for Discrete Interest Periods
-
To convert EIR to NAR for discrete interest periods: - -
i = CF*([(1+ieff)^(PF/CF) - 1)
-
-
-EIR to NAR for Continuous Compounding
-
To convert EIR to NAR for continuous compounding: - -
i = ln((1+ieff)^PF)
-
-
-
-
-
-
-Financial Equation
-
NOTE: in the equations below for the financial transaction, all interest rates -are the effective interest rate, ieff. The symbol will be shortned to just i. - -
The financial equation used to inter-relate n,i,PV,PMT and FV is: - -
1) PV*(1 + i)^n + PMT*(1 + iX)*[(1+i)^n - 1]/i + FV = 0 - -
- Where: X == 0 for end of period payments, and - X == 1 for beginning of period payments - n == number of payment periods - i == effective interest rate for payment period - PV == Present Value - PMT == periodic payment - FV == Future Value -- - - -
The derivation of the financial equation is contained in the
-Financial Equations
-section.
-
-
-
-
-
-Amortization Schedules.
-
-
-Effective and Initial Payment Dates
-
Financial Transactions have an effective Date, ED, and an Initial Payment -Date, IP. ED may or may not be the same as IP, but IP is always the same -or later than ED. Most financial transaction calculators assume that -IP is equal to ED for beginning of period payments or at the end of the -first payment period for end of period payments. - -
This is not always true. IP may be delayed for financial reasons such as cash
-flow or accounting calendar. The subsequent payments then follow the
-agreed upon periodicity.
-
-
-Effective Present Value
-
Since money has a time value, the "delayed" IP -must be accounted for. Computing an "Effective PV", pve, is one means of -handling a delayed IP. - -
If - -
-ED_jdn == the Julian Day Number of ED, and -IP_jdn == the Julian Day Number of IP -- -
pve is computed as: - -
- pve = pv*(1 + i)^(s*PF/d*CF) - - Where: d = length of the payment period in days, and - s = IP_jdn - ED_jdn - d*(1 - X) -- - -
Computing an amortization Schedule for a given financial transaction is -simply applying the basic equation iteratively for each payment period: - -
- PV[n] = PV[n-1] + (PMT + (PV[n-1] + X * PMT) * i) - = PV[n-1] * (1 + i) + PMT * (1 + iX) - for n >= 1 -- -
At the end of each iteration, PV[n] is rounded to the nearest cent. For -each payment period, the interest due may be computed separately as: - -
- ID[n] = (PV[n-1] + X * PMT) * i -- -
and rounded to the nearest cent. PV[n] then becomes: - -
- PV[n] = PV[n-1] + PMT + ID[n] -- - -
For those cases where a yearly summary only is desired, it is not necessary -to compute each transaction for each payment period, rather the PV may be -be computed for the beginning of each year, PV[yr], and the FV computed for -the end of the year, FV[yr]. The interest paid during the year is the computed as: - -
- ID[yr] = (NP * PMT) + PV[yr] + FV[yr] - where: NP == number of payments during year - == PF for a full year of payments -- - -
Since the final payment may not be equal to the periodic payment, the final -payment must be computed separately as follows. Two derivations are given below -for the final payment equation. Both derivations are given below since one or -the other may be clearer to some readers. Both derivations are essentially -the same, they just have different starting points. The first is the fastest to derive. - -
Note, for the purposes of computing an amortization table, the number of periodic -payments is assumed to be an integral value. For most cases this is true, the two -principles in any transaction usually agree upon a certain term or number of periodic -payments. In some calculations, however, this may not hold. In all of the calculations -below, n is assumed integral and in the gnucash implementation, the following calculation -is performed to assure this fact: - -
- n = int(n) -- -
From the basic financial equation derived above: - -
- PV[n] = PV[n-1]*(1 + i) + final_pmt * (1 + iX), i == effective interest rate -- -
solving for final_pmt, we have: -
NOTE: FV[n] = -PV[n], for any n - -
- final_pmt * (1 + iX) = PV[n] - PV[n-1]*(1 + i) - = FV[n-1]*(1 + i) - FV[n] - final_pmt = FV[n-1]*(1+i)/(1 + iX) - FV[n]/(1 + iX) - - final_pmt = FV[n-1]*(1 + i) - FV[n], for X == 0, end of period payments - = FV[n-1] - FV[n]/(1 + i), for X == 1, beginning of period payments -- -
- i[n] == interest due @ payment n - i[n] = (PV[n-1] + X * final_pmt) * i, i == effective interest rate - = (X * final_pmt - FV[n]) * i -- -
Now the final payment is the sum of the interest due, plus the present value -at the next to last payment plus any residual future value after the last payment: - -
- final_pmt = -i[n] - PV[n-1] - FV[n] - = FV[n-1] - i[n] - FV[n] - = FV[n-1] - (X *final_pmt - FV[n-1])*i - FV[n] - = FV[n-1]*(1 + i) - X*final_pmt*i - FV[n] -- -
solving for final_pmt: - -
- final_pmt*(1 + iX) = FV[n-1]*(1 + i) - FV[n] - final_pmt = FV[n-1]*(1 + i)/(1 + iX) - FV[n]/(1 + iX) - - final_pmt = FV[n-1]*(1 + i) - FV[n], for X == 0, end of period payments - = FV[n-1] - FV[n]/(1 + i), for X == 1, beginning of period payments --
The amortization schedule is computed for six different situations: - -
The amortization schedule may be computed and displayed in three manners: - -
At the end of each year a summary is computed and displayed -and the total interest paid is displayed at the end. - -
The total interest paid is displayed at the end. - -
In this amortization schedule, the principal for the -next payment is computed and added into the current payment. This method will -cut the number of total payments in half and will cut the interest paid almost -in half. -
For mortgages, this method of prepayment has the advantage of keeping -the total payments small during the initial payment periods -The payments grow until the last payment period when presumably the borrower -can afford larger payments. -
NOTE: For Payment Frequencies, PF, semi-monthly or less, i.e., PF == 12 or PF == 24,
-a 360 day calendar year and 30 day month are used. For Payment Frequencies, PF,
-greater than semi-monthly, PF > 24, the actual number of days per year and per payment
-period are used. The actual values are computed using the built-in 'jdn' function
-
-
-
-Financial Calculator Usage
-
the Financial Calculator is run as a QTAwk utility. If input is to be interactive and -from the keyboard, do not specify any input files on the command line. The financial -calcutlator reads all input from the standard input file. The calculator is started -as: - -
-QTAwk -f fin.exp -- -
The calculator will clear the display screen and display a two screen help: - -
-Financial Calculator -Copyright (C) 1990 - 1997 Terry D. Boldt, All Rights Reserved. -To compute Loan Quantities: -N ==> to compute # payment periods from i, pv, pmt, fv -_N(i,pv,pmt,fv,CF,PF,disc,bep) ==> to compute # payment periods -I ==> to compute nominal interest rate from n, pv, pmt, fv, CF, PF, disc, bep -_I(n,pv,pmt,fv,CF,PF,disc,bep) ==> to compute interest -PV ==> to compute Present Value from n, i, pmt, fv, CF, PF, disc, bep -_PV(n,i,pmt,fv) ==> to compute Present Value -PMT ==> to compute Payment from n, i, pv, fv, CF, PF, disc, bep -_PMT(n,i,pv,fv,CF,PF,disc,bep) ==> to compute Payment -FV ==> to compute Future Value from n, i, pv, pmt, CF, PF, disc, bep -_FV(n,i,pv,pmt,CF,PF,disc,bep) ==> to compute Future Value -Press Any Key to Continue -- -
The first screen displays the calculator commands which are available. Press any key -and a second screen displays the variables defined by the calculator and which must be -set by the user to use the financial calculator functions. - -
-[Aa](mort)? to Compute Amortization Schedule -[Cc](ls)? to Clear Screen -[Dd](efault)? to Re-Initialize -[Hh](elp) to Display This Help -[Qq](uit)? to Quit -[Ss](tatus)? to Display Status of Computations -[Uu](ser) Display User Defined Variables - -Variables to set: -n == number of periodic payments -i == interest per compouding interval -pv == present value -pmt == periodic payment -fv == future value -disc == TRUE/FALSE == discrete/continuous compounding -bep == TRUE/FALSE == beginning of period/end of period payments -CF == compounding frequency per year -PF == payment frequency per year - -ED == effective date of transaction, mm/dd/yyyy -IP == initial payment date of transaction, mm/dd/yyyy -- - -
The financial calculator commands available are listed above and below. - -
Note that the first letter of the command is all that is necessary to activate the -desired function. - -
-Financial Calculator -Copyright (C) 1990 - 1997 Terry D. Boldt, All Rights Reserved -Current Financial Calculator Status: -Compounding Frequency: (CF) 12 -Payment Frequency: (PF) 12 -Compounding: Discrete (disc = TRUE) -Payments: End of Period (bep = FALSE) -Number of Payment Periods (n): 360 (Years: 30) -Nominal Annual Interest Rate (i): 7.25 - Effective Interest Rate Per Payment Period: 0.00604167 -Present Value (pv): 233,350.00 -Periodic Payment (pmt): -1,591.86 -Future Value (fv): 0.00 -Effective Date: Tue Jun 04 00:00:00 1996(2450239) -Initial Payment Date: Thu Aug 01 00:00:00 1996(2450297) -<> --
The calculator displays an input prompt whenever it is waiting for input -from the keyboard. The input prompt is simply <>. The desired -input is typed at the keyboard and the enter key pressed. The result of calculating the -value of the input line is then displayed by the calculator. For example, if the user wanted -to set the value of the nominal interest in the calculator to 6.25, the following line would be -input to the calculator: - -
i=6.25. - -
A semi-colon at the end of the input is optional. -The line as seen on the display with the calculator input prompt would be: - -
-<>i = 6.25 - 6.25 -- -
Note that the calculator displays the value of the result, 6.25 in this case. - -
The calculator is controlled by setting the calculator variables to the desired values -and "executing" the calculator functions to derive the values for the unknown -variables. For example, for a conventional home mortgage for $233,350.00 with a thirty year -term, nominal annual rate of 7.25%, n, i, pv and fv are known: - -
-n == 360 == 12 * 30 -i == 7.25 -pv= 233350 -fv = 0 -- -
The payments to completely pay off the mortgage with the 360 periodic payments is desired. -To compute the desired periodic payment value, the PMT function is used. Since the -function has no defined arguments, in invoking the function no arguments are specified. The -complete session to input the desired values and calculate the periodic payment value would -appear as: - -
-<>n=30*12 - 360 -<>i=7.25 - 7.25 -<>pv=233350 - 233,350 -<>PMT - -1,591.86 -- -
Note that the input may contain computations, n=30*12. In addition, any QTAwk -built-in function may be specified and any functions defined in the financial calculator. -This can be handy for computing intermediate values or other results from the results of -the calculator. - -
Note that the output of the PMT function is rounded to the nearest cent. Over the -thirty year term of the payback, the rounding will affect the last payment. To determine -the balance due, fv, after 359 payment have been made, decrement n by 1 and compute the -future value: - -
-<>n-=1 - 359 -<>FV - -1,580.20 -<>n+=1 - 360 -<>FV - 2.12 -<> -- -
The future value after 359 payments is less than the periodic payment and a full final payment
-will overpay the loan. The final FV computation with n restored to 360 shows an overpayment
-of 2.12.
-
-
-Calculator Functions
-
The calculator functions: - -
-N -I -PV -PMT -FV -- -
can be used to calculate the variable with the corresponding lower case name, using the -values of the other four calculator variables which have already been set. In addition, the -calculator functions: - -
-_N(i,pv,pmt,fv,CF,PF,disc,bep) -_I(n,pv,pmt,fv,CF,PF,disc,bep) -_PV(n,i,pmt,fv,CF,PF,disc,bep) -_PMT(n,i,pv,fv,CF,PF,disc,bep) -_FV(n,i,pv,pmt,CF,PF,disc,bep) -- -
can be used to compute the value of the corresponding quantity for any specified value -of the input arguments. - -
There are three differences between the functions N, I, PV, PMT, FV and the -functions -_N(i,pv,pmt,fv,CF,PF,disc,bep), _I(n,pv,pmt,fv,CF,PF,disc,bep), _PV(n,i,pmt,fv,CF,PF,disc,bep), -_PMT(n,i,pv,fv,CF,PF,disc,bep), _FV(n,i,pv,pmt,CF,PF,disc,bep). -
User defined variables may be defined and their values set to a desired qunatity. For example, -to save computation results before re-initializing the calculator to obtain other results. If -the user desired to compare the periodic payments necessary to fully pay the conventional -mortgage cited above, the payment computed above could be saved in the variable -end_pmt, the payments set to beginning of period payments and the new payment -computed. The new value could be set into the variable beg_pmt. The two payments -could then be viewed with the u command. The difference could then be computed -between the two payment methods: - -
-<>n=30*12 - 360 -<>i=7.25 - 7.25 -<>pv=233350 - 233,350 -<>PMT - -1,591.86 -<>end_pmt=pmt - -1,591.86 -<>bep=1 - 1 -<>PMT - -1,582.30 -<>beg_pmt=pmt - -1,582.30 -<>u - -Financial Calculator -Copyright (C) 1990 - 1997 Terry D. Boldt, All Rights Reserved. -Current Financial Calculator Status: -User Defined Variables: -end_pmt == -1,591.86 -beg_pmt == -1,582.30 -<>beg_pmt-end_pmt - 9.56 -<> -- -
The financial calculator is thus a true calculator and can be used for computations
-desired by the user beyond those performed by the functions of the utility.
-
-
-Rounding
-
Note that the output of the calculator is rounded to the nearest cent for floating -point values. Sometimes the full accuracy of the value is desired. This can be obtained -by redefing the calculator variable ofmt to the string "%.15g". You might want to -save the current value in a user variable for resetting. For example in the above -conventional mortgage, the exact value of the periodic payment can be displayed as: - -
-<>sofmt=ofmt - "%.2f" -<>ofmt="%.15g" - "%.15g" -<>pmt=_PMT(n,i,pv,fv,CF,PF,disc,bep) - -1,591.85834951112 -<>ofmt=sofmt - "%.2f" -<> -- -
Note that the current value of the output format string, ofmt, has been
-saved in the variable, sofmt, and later restored.
-
-
-Examples
-
-
-
-
-
-
-
-
-
-
-Simple Interest
-
Simple Interest -
Find the annual simple interest rate (%) for an $800 loan to be repayed at the - end of one year with a single payment of $896. -
- <>d - <>CF=PF=1 - 1 - <>n=1 - 1 - <>pv=-800 - -800 - <>fv=896 - 896 - <>I - 12.00 -- - -
Compound Interest -
Find the future value of $800 after one year at a nominal rate of 12% - compounded monthly. No payments are specified, so the payment frequency is - set equal to the compounding frequency at the default values. -
- <>d - <>n=12 - 12 - <>i=12 - 12 - <>pv=-800 - -800 - <>FV - 901.46 -- - -
Periodic Payment -
Find the monthly end-of-period payment required to fully amortize the loan - in Example 2. A fully amortized loan has a future value of zero. -
- <>fv=0 - 0 - <>PMT - 71.08 -- - -
Conventional Mortgage -
Find the number of monthly payments necessary to fully amortize a loan of - $100,000 at a nominal rate of 13.25% compounded monthly, if monthly end-of-period - payments of $1125.75 are made. -
- <>d - <>i=13.25 - 13.25 - <>pv=100000 - 100,000 - <>pmt=-1125.75 - -1,125.75 - <>N - 360.10 -- - -
Final Payment -
Using the data in the above example, find the amount of the final payment if n is -changed to 360. The final payment will be equal to the regular payment plus -any balance, future value, remaining at the end of period number 360. -
- <>n=int(n) - 360 - <>FV - -108.87 - <>pmt+fv - -1,234.62 -- - -
Conventional Mortgage Amortization Schedule - Annual Summary -
Using the data from the loan in the previous example, compute the amortization -schedule when the -Effective date of the loan is June 6, 1996 and the initial payment is -made on August 1, 1996. Ignore any change in the PV due to the delayed -initial payment caused by the partial payment period from June 6 to July 1. - -
- <>ED=6/6/1996 - Effective Date set: (2450241) Thu Jun 06 00:00:00 1996 - <>IP=8/1/96 - Initial Payment Date set: (2450297) Thu Aug 01 00:00:00 1996 - <>a - Effective Date: Thu Jun 06 00:00:00 1996 - Initial Payment Date: Thu Aug 01 00:00:00 1996 - The amortization options are: - The Old Present Value (pv) was: 100,000.00 - The Old Periodic Payment (pmt) was: -1,125.75 - The Old Future Value (fv) was: -108.87 - 1: Amortize with Original Transaction Values - and final payment: -1,125.75 - - The New Present Value (pve) is: 100,919.30 - The New Periodic Payment (pmt) is: -1,136.10 - 2: Amortize with Original Periodic Payment - and final payment: -49,023.68 - 3: Amortize with New Periodic Payment - and final payment: -1,132.57 - 4: Amortize with Original Periodic Payment, - new number of total payments (n): 417 - and final payment: -2,090.27 - - Enter choice 1, 2, 3 or 4: <> -- -
Press '1' to choose option 1: - -
- Amortization Schedule: - Yearly, y, per Payment, p, or Advanced Payment, a, Amortization - Enter choice y, p or a: - <> -- -
Press 'y' for an annual summary: - -
- Enter Filename for Amortization Schedule. - (null string uses Standard Output): -- -
Press enter to display output on screen: - -
- Amortization Table - Effective Date: Thu Jun 06 00:00:00 1996 - Initial Payment Date: Thu Aug 01 00:00:00 1996 - Compounding Frequency per year: 12 - Payment Frequency per year: 12 - Compounding: Discrete - Payments: End of Period - Payments (359): -1,125.75 - Final payment (# 360): -1,125.75 - Nominal Annual Interest Rate: 13.25 - Effective Interest Rate Per Payment Period: 0.0110417 - Present Value: 100,000.00 - Year Interest Ending Balance - 1996 -5,518.42 -99,889.67 - 1997 -13,218.14 -99,598.81 - 1998 -13,177.17 -99,266.98 - 1999 -13,130.43 -98,888.41 - 2000 -13,077.11 -98,456.52 - 2001 -13,016.28 -97,963.80 - 2002 -12,946.88 -97,401.68 - 2003 -12,867.70 -96,760.38 - 2004 -12,777.38 -96,028.76 - 2005 -12,674.33 -95,194.09 - 2006 -12,556.76 -94,241.85 - 2007 -12,422.64 -93,155.49 - 2008 -12,269.63 -91,916.12 - 2009 -12,095.06 -90,502.18 - 2010 -11,895.91 -88,889.09 - 2011 -11,668.70 -87,048.79 - 2012 -11,409.50 -84,949.29 - 2013 -11,113.78 -82,554.07 - 2014 -10,776.41 -79,821.48 - 2015 -10,391.53 -76,704.01 - 2016 -9,952.43 -73,147.44 - 2017 -9,451.49 -69,089.93 - 2018 -8,879.99 -64,460.92 - 2019 -8,227.99 -59,179.91 - 2020 -7,484.16 -53,155.07 - 2021 -6,635.56 -46,281.63 - 2022 -5,667.43 -38,440.06 - 2023 -4,562.94 -29,494.00 - 2024 -3,302.89 -19,287.89 - 2025 -1,865.36 -7,644.25 - 2026 -236.00 -108.87 - - Total Interest: -305,270.00 -- -
NOTE: The amortization table leaves the FV as it was when the amortization -function was entered. Thus, a balance of 108.87 is due at the end of the -table. To completely pay the loan, set fv to 0.0: -
-<>fv=0 - 0 -<>a - Effective Date: Thu Jun 06 00:00:00 1996 - Initial Payment Date: Thu Aug 01 00:00:00 1996 - The amortization options are: - The Old Present Value (pv) was: 100,000.00 - The Old Periodic Payment (pmt) was: -1,125.75 - The Old Future Value (fv) was: 0.00 - 1: Amortize with Original Transaction Values - and final payment: -1,234.62 - - The New Present Value (pve) is: 100,919.30 - The New Periodic Payment (pmt) is: -1,136.12 - 2: Amortize with Original Periodic Payment - and final payment: -49,132.55 - 3: Amortize with New Periodic Payment - and final payment: -1,148.90 - 4: Amortize with Original Periodic Payment, - new number of total payments (n): 417 - and final payment: -2,199.14 - - Enter choice 1, 2, 3 or 4: <> -- -
Press '1' for option 1: - -
- Amortization Schedule: - Yearly, y, per Payment, p, or Advanced Payment, a, Amortization - Enter choice y, p or a: - <> -- -
Press 'y' for annual summary: - -
- Enter Filename for Amortization Schedule. - (null string uses Standard Output): -- -
Press enter to display output on screen: - -
- Amortization Table - Effective Date: Thu Jun 06 00:00:00 1996 - Initial Payment Date: Thu Aug 01 00:00:00 1996 - Compounding Frequency per year: 12 - Payment Frequency per year: 12 - Compounding: Discrete - Payments: End of Period - Payments (359): -1,125.75 - Final payment (# 360): -1,234.62 - Nominal Annual Interest Rate: 13.25 - Effective Interest Rate Per Payment Period: 0.0110417 - Present Value: 100,000.00 - Year Interest Ending Balance - 1996 -5,518.42 -99,889.67 - 1997 -13,218.14 -99,598.81 - 1998 -13,177.17 -99,266.98 - 1999 -13,130.43 -98,888.41 - 2000 -13,077.11 -98,456.52 - 2001 -13,016.28 -97,963.80 - 2002 -12,946.88 -97,401.68 - 2003 -12,867.70 -96,760.38 - 2004 -12,777.38 -96,028.76 - 2005 -12,674.33 -95,194.09 - 2006 -12,556.76 -94,241.85 - 2007 -12,422.64 -93,155.49 - 2008 -12,269.63 -91,916.12 - 2009 -12,095.06 -90,502.18 - 2010 -11,895.91 -88,889.09 - 2011 -11,668.70 -87,048.79 - 2012 -11,409.50 -84,949.29 - 2013 -11,113.78 -82,554.07 - 2014 -10,776.41 -79,821.48 - 2015 -10,391.53 -76,704.01 - 2016 -9,952.43 -73,147.44 - 2017 -9,451.49 -69,089.93 - 2018 -8,879.99 -64,460.92 - 2019 -8,227.99 -59,179.91 - 2020 -7,484.16 -53,155.07 - 2021 -6,635.56 -46,281.63 - 2022 -5,667.43 -38,440.06 - 2023 -4,562.94 -29,494.00 - 2024 -3,302.89 -19,287.89 - 2025 -1,865.36 -7,644.25 - 2026 -344.87 0.00 - - Total Interest: -305,378.87 -- -
Note that now the final payment differs from the periodic payment and
-the loan has been fully paid off.
-
-
-Conventional Mortgage Amortization Schedule - Periodic Payment Schedule
-
Conventional Mortgage Amortization Schedule - Periodic Payment Schedule -
Using the loan in the previous example, compute the amortization table and display the -results for each payment period. -As in example 6, ignore any increase in the PV due to the -delayed IP. - -
-<> - Amortization Table - Effective Date: Thu Jun 06 00:00:00 1996 - Initial Payment Date: Thu Aug 01 00:00:00 1996 - Compounding Frequency per year: 12 - Payment Frequency per year: 12 - Compounding: Discrete - Payments: End of Period - Payments (359): -1,125.75 - Final payment (# 360): -1,234.62 - Nominal Annual Interest Rate: 13.25 - Effective Interest Rate Per Payment Period: 0.0110417 - Present Value: 100,000.00 - Pmt# Interest Principal Balance - 1 -1,104.17 -21.58 -99,978.42 - 2 -1,103.93 -21.82 -99,956.60 - 3 -1,103.69 -22.06 -99,934.54 - 4 -1,103.44 -22.31 -99,912.23 - 5 -1,103.20 -22.55 -99,889.68 - Summary for 1996: - Interest Paid: -5,518.43 - Principal Paid: -110.32 - Year Ending Balance: -99,889.68 - Sum of Interest Paid: -5,518.43 - Pmt# Interest Principal Balance - 6 -1,102.95 -22.80 -99,866.88 - 7 -1,102.70 -23.05 -99,843.83 - 8 -1,102.44 -23.31 -99,820.52 - 9 -1,102.18 -23.57 -99,796.95 - 10 -1,101.92 -23.83 -99,773.12 - 11 -1,101.66 -24.09 -99,749.03 - 12 -1,101.40 -24.35 -99,724.68 - 13 -1,101.13 -24.62 -99,700.06 - 14 -1,100.85 -24.90 -99,675.16 - 15 -1,100.58 -25.17 -99,649.99 - 16 -1,100.30 -25.45 -99,624.54 - 17 -1,100.02 -25.73 -99,598.81 - Summary for 1997: - Interest Paid: -13,218.13 - Principal Paid: -290.87 - Year Ending Balance: -99,598.81 - Sum of Interest Paid: -18,736.56 - Pmt# Interest Principal Balance - 18 -1,099.74 -26.01 -99,572.80 - 19 -1,099.45 -26.30 -99,546.50 - . - . - . - 346 -171.99 -953.76 -14,622.84 - 347 -161.46 -964.29 -13,658.55 - 348 -150.81 -974.94 -12,683.61 - 349 -140.05 -985.70 -11,697.91 - 350 -129.16 -996.59 -10,701.32 - 351 -118.16 -1,007.59 -9,693.73 - 352 -107.03 -1,018.72 -8,675.01 - 353 -95.79 -1,029.96 -7,645.05 - Summary for 2025: - Interest Paid: -1,865.45 - Principal Paid: -11,643.55 - Year Ending Balance: -7,645.05 - Sum of Interest Paid: -305,034.80 - Pmt# Interest Principal Balance - 354 -84.41 -1,041.34 -6,603.71 - 355 -72.92 -1,052.83 -5,550.88 - 356 -61.29 -1,064.46 -4,486.42 - 357 -49.54 -1,076.21 -3,410.21 - 358 -37.65 -1,088.10 -2,322.11 - 359 -25.64 -1,100.11 -1,222.00 - Final Payment (360): -1,235.49 - 360 -13.49 -1,222.00 0.00 - Summary for 2026: - Interest Paid: -344.94 - Principal Paid: -7,645.05 - - Total Interest: -305,379.74 -- -
The complete amortization table can be viewed in the -Periodic Amortization Schedule for this loan. - -
You will notice several differences between this amortization schedule and the -Annual Summary Schedule. The Periodic Payment Schedule lists the interest paid for -each payment as well as the principal paid and the remaining balance to be repaid. -At the end of each year an annual summary is printed. At the end of the table the -total interest is printed as in the Annual Summary Schedule. - -
You will notice that the total interest output at the end of the Periodic Payment -Schedule differs slightly from the total interest output at the end of the Annual Summary -Schedule: - -
Total Interest for Periodic Payment Schedule: -
- Total Interest: -305,379.74 -- -
Total Interest for Annual Summary Schedule: - -
- Total Interest: -305,378.87 -- -
The difference in total interest is due to the rounding of all quantities at
-each periodic payment. The Total Interest paid shown in the Periodic Payment
-Schedule will be the more accurate since all quantities exchanged in a financial
-transaction will be done to the nearest cent.
-
-
-Conventional Mortgage Schedule - Variable Advanced Payments
-
Conventional Mortgage Schedule - Variable Advanced Payments -
Again using the loan in the previous examples, compute the amortization table using -the advanced payment -option to prepay the loan. As in the previous example, ignore any increase in the PV due to the -delayed IP. - -
- - Effective Date: Thu Jun 06 00:00:00 1996 - Initial Payment Date: Thu Aug 01 00:00:00 1996 - The amortization options are: - The Old Present Value (pv) was: 100,000.00 - The Old Periodic Payment (pmt) was: -1,125.75 - The Old Future Value (fv) was: 0.00 - 1: Amortize with Original Transaction Values - and final payment: -1,234.62 - - The New Present Value (pve) is: 100,919.30 - The New Periodic Payment (pmt) is: -1,136.12 - 2: Amortize with Original Periodic Payment - and final payment: -49,132.55 - 3: Amortize with New Periodic Payment - and final payment: -1,148.90 - 4: Amortize with Original Periodic Payment, - new number of total payments (n): 417 - and final payment: -2,199.14 - - Enter choice 1, 2, 3 or 4: <> -- -
Press 1 for option 1: - -
- Amortization Schedule: - Yearly, y, per Payment, p, or Advanced Payment, a, Amortization - Enter choice y, p or a: - <> -- -
Press a for the Advanced Payment Option: - -
- Enter Filename for Amortization Schedule. - (null string uses Standard Output): -- -
Press enter to display output on screen: - -
- Amortization Table - Effective Date: Thu Jun 06 00:00:00 1996 - Initial Payment Date: Thu Aug 01 00:00:00 1996 - Compounding Frequency per year: 12 - Payment Frequency per year: 12 - Compounding: Discrete - Payments: End of Period - Payments (359): -1,125.75 - Final payment (# 360): -1,234.62 - Nominal Annual Interest Rate: 13.25 - Effective Interest Rate Per Payment Period: 0.0110417 - Present Value: 100,000.00 - Advanced Prepayment Amortization - Pmt# Interest Principal Prepay Total Pmt Balance - 1 -1,104.17 -21.58 -21.82 -1,147.57 -99,956.60 - 2 -1,103.69 -22.06 -22.31 -1,148.06 -99,912.23 - 3 -1,103.20 -22.55 -22.80 -1,148.55 -99,866.88 - 4 -1,102.70 -23.05 -23.31 -1,149.06 -99,820.52 - 5 -1,102.18 -23.57 -23.83 -1,149.58 -99,773.12 - Summary for 1996: - Interest Paid: -5,515.94 - Principal Paid: -226.88 - Year Ending Balance: -99,773.12 - Sum of Interest Paid: -5,515.94 - Pmt# Interest Principal Prepay Total Pmt Balance - 6 -1,101.66 -24.09 -24.35 -1,150.10 -99,724.68 - 7 -1,101.13 -24.62 -24.90 -1,150.65 -99,675.16 - 8 -1,100.58 -25.17 -25.45 -1,151.20 -99,624.54 - 9 -1,100.02 -25.73 -26.01 -1,151.76 -99,572.80 - 10 -1,099.45 -26.30 -26.59 -1,152.34 -99,519.91 - 11 -1,098.87 -26.88 -27.18 -1,152.93 -99,465.85 - 12 -1,098.27 -27.48 -27.78 -1,153.53 -99,410.59 - 13 -1,097.66 -28.09 -28.40 -1,154.15 -99,354.10 - 14 -1,097.03 -28.72 -29.03 -1,154.78 -99,296.35 - 15 -1,096.40 -29.35 -29.68 -1,155.43 -99,237.32 - 16 -1,095.75 -30.00 -30.34 -1,156.09 -99,176.98 - 17 -1,095.08 -30.67 -31.01 -1,156.76 -99,115.30 - Summary for 1997: - Interest Paid: -13,181.90 - Principal Paid: -657.82 - Year Ending Balance: -99,115.30 - Sum of Interest Paid: -18,697.84 - Pmt# Interest Principal Prepay Total Pmt Balance - 18 -1,094.40 -31.35 -31.70 -1,157.45 -99,052.25 - 19 -1,093.70 -32.05 -32.40 -1,158.15 -98,987.80 - 20 -1,092.99 -32.76 -33.12 -1,158.87 -98,921.92 - . - . - . - 167 -298.87 -826.88 -836.01 -1,961.76 -25,404.90 - 168 -280.51 -845.24 -854.57 -1,980.32 -23,705.09 - 169 -261.74 -864.01 -873.55 -1,999.30 -21,967.53 - 170 -242.56 -883.19 -892.94 -2,018.69 -20,191.40 - 171 -222.95 -902.80 -912.77 -2,038.52 -18,375.83 - 172 -202.90 -922.85 -933.04 -2,058.79 -16,519.94 - 173 -182.41 -943.34 -953.76 -2,079.51 -14,622.84 - Summary for 2010: - Interest Paid: -3,448.07 - Principal Paid: -20,232.96 - Year Ending Balance: -14,622.84 - Sum of Interest Paid: -152,300.57 - Pmt# Interest Principal Prepay Total Pmt Balance - 174 -161.46 -964.29 -974.94 -2,100.69 -12,683.61 - 175 -140.05 -985.70 -996.59 -2,122.34 -10,701.32 - 176 -118.16 -1,007.59 -1,018.72 -2,144.47 -8,675.01 - 177 -95.79 -1,029.96 -1,041.34 -2,167.09 -6,603.71 - 178 -72.92 -1,052.83 -1,064.46 -2,190.21 -4,486.42 - 179 -49.54 -1,076.21 -1,088.10 -2,213.85 -2,322.11 - 180 -25.64 -1,100.11 -1,222.00 -2,347.75 0.00 - Summary for 2011: - Interest Paid: -663.56 - Principal Paid: -14,622.84 - - Total Interest: -152,964.13 -- -
The complete amortization table can be viewed in the -Advanced Payment Amortization Schedule for this loan. - -
This schedule has added two columns over the Periodic Payment Schedule in Example 7. Namely,
-Prepay and the Total Pmt columns. The Prepay column is the
-amount of the loan prepayment for the period. The Total Pmt column is the sum
-of the periodic payment and the Prepayment. Note that both the Prepay and the
-Total Pmt quantities increase with each period.
-
-
-Conventional Mortgage Schedule - Constant Advanced Payments
-
Conventional Mortgage Schedule - Constant Advanced Payments -
Using the loan in the previous examples, compute the amortization table using -another payment option for repaying a loan ahead of schedule and reducing the interest -paid, constant repayments at each periodic payment. Suppose a constant $100.00 is paid -towards the principal with each periodic payment. How many payments are needed to fully payoff -the loan and what is the total interest paid? - -
As in the previous example, ignore any increase in the PV due to the -delayed IP. - -
There are two ways to compute the amortization table for this type of prepayment option. -In the first method, set the variable 'FP' to the amount of the monthly prepayment. - -
-<>FP=-100 - -100 -<>a - Effective Date: Thu Jun 06 00:00:00 1996 - Initial Payment Date: Thu Aug 01 00:00:00 1996 - The amortization options are: - The Old Present Value (pv) was: 100,000.00 - The Old Periodic Payment (pmt) was: -1,125.75 - The Old Future Value (fv) was: 0.00 - 1: Amortize with Original Transaction Values - and final payment: -1,234.62 - - The New Present Value (pve) is: 100,919.30 - The New Periodic Payment (pmt) is: -1,136.12 - 2: Amortize with Original Periodic Payment - and final payment: -49,132.55 - 3: Amortize with New Periodic Payment - and final payment: -1,148.90 - 4: Amortize with Original Periodic Payment, - new number of total payments (n): 417 - and final payment: -2,199.14 - - Enter choice 1, 2, 3 or 4: <> -- -
Press 1 for option 1: - -
- Amortization Schedule: - Yearly, y, per Payment, p, Advanced Payment, a, or Fixed Prepayment, f, Amortization - Enter choice y, p, a or f: - <> -- -
Press f for the Fixed Prepayment schedule. - -
- Enter Filename for Amortization Schedule. - (null string uses Standard Output): -- -
Press enter to display output on screen: - -
-Amortization Table -Effective Date: Thu Jun 6 00:00:00 1996 -Initial Payment Date: Thu Aug 1 00:00:00 1996 -Compounding Frequency per year: 12 -Payment Frequency per year: 12 -Compounding: Discrete -Payments: End of Period -Payments (359): -1,125.75 -Final payment (# 360): -1,234.62 -Nominal Annual Interest Rate: 13.25 - Effective Interest Rate Per Payment Period: 0.0110417 -Present Value: 100,000.00 -Advanced Prepayment Amortization - fixed prepayment: -100.00 -Pmt# Interest Principal Prepay Total Pmt Balance - 1 -1,104.17 -21.58 -100.00 -1,225.75 -99,878.42 - 2 -1,102.82 -22.93 -100.00 -1,225.75 -99,755.49 - 3 -1,101.47 -24.28 -100.00 -1,225.75 -99,631.21 - 4 -1,100.09 -25.66 -100.00 -1,225.75 -99,505.55 - 5 -1,098.71 -27.04 -100.00 -1,225.75 -99,378.51 -Summary for 1996: - Interest Paid: -5,507.26 - Principal Paid: -621.49 - Year Ending Balance: -99,378.51 - Sum of Interest Paid: -5,507.26 -Pmt# Interest Principal Prepay Total Pmt Balance - 6 -1,097.30 -28.45 -100.00 -1,225.75 -99,250.06 - 7 -1,095.89 -29.86 -100.00 -1,225.75 -99,120.20 - 8 -1,094.45 -31.30 -100.00 -1,225.75 -98,988.90 - 9 -1,093.00 -32.75 -100.00 -1,225.75 -98,856.15 - 10 -1,091.54 -34.21 -100.00 -1,225.75 -98,721.94 - 11 -1,090.05 -35.70 -100.00 -1,225.75 -98,586.24 - 12 -1,088.56 -37.19 -100.00 -1,225.75 -98,449.05 - 13 -1,087.04 -38.71 -100.00 -1,225.75 -98,310.34 - 14 -1,085.51 -40.24 -100.00 -1,225.75 -98,170.10 - 15 -1,083.96 -41.79 -100.00 -1,225.75 -98,028.31 - 16 -1,082.40 -43.35 -100.00 -1,225.75 -97,884.96 - 17 -1,080.81 -44.94 -100.00 -1,225.75 -97,740.02 -Summary for 1997: - Interest Paid: -13,070.51 - Principal Paid: -1,638.49 - Year Ending Balance: -97,740.02 - Sum of Interest Paid: -18,577.77 -. -. -. - -Pmt# Interest Principal Prepay Total Pmt Balance - 186 -298.60 -827.15 -100.00 -1,225.75 -26,115.84 - 187 -288.36 -837.39 -100.00 -1,225.75 -25,178.45 - 188 -278.01 -847.74 -100.00 -1,225.75 -24,230.71 - 189 -267.55 -858.20 -100.00 -1,225.75 -23,272.51 - 190 -256.97 -868.78 -100.00 -1,225.75 -22,303.73 - 191 -246.27 -879.48 -100.00 -1,225.75 -21,324.25 - 192 -235.46 -890.29 -100.00 -1,225.75 -20,333.96 - 193 -224.52 -901.23 -100.00 -1,225.75 -19,332.73 - 194 -213.47 -912.28 -100.00 -1,225.75 -18,320.45 - 195 -202.29 -923.46 -100.00 -1,225.75 -17,296.99 - 196 -190.99 -934.76 -100.00 -1,225.75 -16,262.23 - 197 -179.56 -946.19 -100.00 -1,225.75 -15,216.04 -Summary for 2012: - Interest Paid: -2,882.05 - Principal Paid: -11,826.95 - Year Ending Balance: -15,216.04 - Sum of Interest Paid: -156,688.79 -Pmt# Interest Principal Prepay Total Pmt Balance - 198 -168.01 -957.74 -100.00 -1,225.75 -14,158.30 - 199 -156.33 -969.42 -100.00 -1,225.75 -13,088.88 - 200 -144.52 -981.23 -100.00 -1,225.75 -12,007.65 - 201 -132.58 -993.17 -100.00 -1,225.75 -10,914.48 - 202 -120.51 -1,005.24 -100.00 -1,225.75 -9,809.24 - 203 -108.31 -1,017.44 -100.00 -1,225.75 -8,691.80 - 204 -95.97 -1,029.78 -100.00 -1,225.75 -7,562.02 - 205 -83.50 -1,042.25 -100.00 -1,225.75 -6,419.77 - 206 -70.88 -1,054.87 -100.00 -1,225.75 -5,264.90 - 207 -58.13 -1,067.62 -100.00 -1,225.75 -4,097.28 - 208 -45.24 -1,080.51 -100.00 -1,225.75 -2,916.77 - 209 -32.21 -1,093.54 -100.00 -1,225.75 -1,723.23 -Summary for 2013: - Interest Paid: -1,216.19 - Principal Paid: -13,492.81 - Year Ending Balance: -1,723.23 - Sum of Interest Paid: -157,904.98 -Pmt# Interest Principal Prepay Total Pmt Balance - 210 -19.03 -1,106.72 -100.00 -1,225.75 -516.51 - 211 -5.70 -516.51 0.00 -522.21 0.00 - -Total Interest: 157,929.71 - -- -
In the second method, the periodic payment is increased by 100. With this method, -the annual summary table can also be computed. - -
-<>s -Financial Calculator -Copyright (C) 1990 - 1997 Terry D. Boldt, All Rights Reserved. -Current Financial Calculator Status: -Compounding Frequency: (CF) 12 -Payment Frequency: (PF) 12 -Compounding: Discrete (disc = TRUE) -Payments: End of Period (bep = FALSE) -Number of Payment Periods (n): 360 (Years: 30) -Nominal Annual Interest Rate (i): 13.25 - Effective Interest Rate Per Payment Period: 0.0110417 -Present Value (pv): 100,000.00 -Periodic Payment (pmt): -1,125.75 -Future Value (fv): 0.00 -Effective Date: Thu Jun 06 00:00:00 1996(2450241) -Initial Payment Date: Thu Aug 01 00:00:00 1996(2450297) -<>pmt-=100 - -1,225.75 -<>N - 210.42 -<> -- -
Thus, the loan will now be fully repaid in 210 full payments and a partial payment -as illustrated in the previous table. -To get the total interest paid, display the Annual Summary Amortization Schedule: - -
-Effective Date: Thu Jun 06 00:00:00 1996 -Initial Payment Date: Thu Aug 01 00:00:00 1996 -The amortization options are: -The Old Present Value (pv) was: 100,000.00 -The Old Periodic Payment (pmt) was: -1,225.75 -The Old Future Value (fv) was: 0.00 -1: Amortize with Original Transaction Values - and final payment: -1,742.55 - -The New Present Value (pve) is: 100,919.30 -The New Periodic Payment (pmt) is: -1,237.02 -2: Amortize with Original Periodic Payment - and final payment: -10,967.39 -3: Amortize with New Periodic Payment - and final payment: -1,757.20 -4: Amortize with Original Periodic Payment, - new number of total payments (n): 218 - and final payment: -1,668.45 - -Enter choice 1, 2, 3 or 4: <> -- -
Press '1' for option 1: - -
- Amortization Schedule: -Yearly, y, per Payment, p, or Advanced Payment, a, Amortization -Enter choice y, p or a: -<> -- -
Press 'y' for an annual Summary - -
-Enter Filename for Amortization Schedule. - (null string uses Standard Output): -- -
Press enter to display the summary on the screen: - -
- Amortization Table - Effective Date: Thu Jun 06 00:00:00 1996 - Initial Payment Date: Thu Aug 01 00:00:00 1996 - Compounding Frequency per year: 12 - Payment Frequency per year: 12 - Compounding: Discrete - Payments: End of Period - Payments (209): -1,225.75 - Final payment (# 210): -1,742.55 - Nominal Annual Interest Rate: 13.25 - Effective Interest Rate Per Payment Period: 0.0110417 - Present Value: 100,000.00 - Year Interest Ending Balance - 1996 -5,507.26 -99,378.51 - 1997 -13,070.52 -97,740.03 - 1998 -12,839.74 -95,870.77 - 1999 -12,576.45 -93,738.22 - 2000 -12,276.08 -91,305.30 - 2001 -11,933.40 -88,529.70 - 2002 -11,542.46 -85,363.16 - 2003 -11,096.45 -81,750.61 - 2004 -10,587.62 -77,629.23 - 2005 -10,007.12 -72,927.35 - 2006 -9,344.86 -67,563.21 - 2007 -8,589.32 -61,443.53 - 2008 -7,727.36 -54,461.89 - 2009 -6,744.00 -46,496.89 - 2010 -5,622.13 -37,410.02 - 2011 -4,342.24 -27,043.26 - 2012 -2,882.08 -15,216.34 - 2013 -1,216.25 -1,723.59 - 2014 -18.96 0.00 - - Total Interest: -157,924.30 -- -
From the last line the Total interest has been decreased from $305,379.74 to -$157,924.30. - -
We can also ask how much of a constant repayment would be necessary to fully -repay the loan in 15 years and what would be the total interest paid? - -
- <>n=12*15 - 180 - <>opmt=pmt - -1,125.75 - <>PMT - -1,281.74 - <>pmt-opmt - -155.99 -- -
Thus, a constant advanced repayment per periodic payment of $155.99 would fully -amortize the loan in 15 years. - -
- <>a - Effective Date: Thu Jun 06 00:00:00 1996 - Initial Payment Date: Thu Aug 01 00:00:00 1996 - The amortization options are: - The Old Present Value (pv) was: 100,000.00 - The Old Periodic Payment (pmt) was: -1,281.74 - The Old Future Value (fv) was: 0.00 - 1: Amortize with Original Transaction Values - and final payment: -1,279.73 - - The New Present Value (pve) is: 100,919.30 - The New Periodic Payment (pmt) is: -1,293.52 - 2: Amortize with Original Periodic Payment - and final payment: -7,915.43 - 3: Amortize with New Periodic Payment - and final payment: -1,293.20 - 4: Amortize with Original Periodic Payment, - new number of total payments (n): 185 - and final payment: -1,738.05 - - Enter choice 1, 2, 3 or 4: <> -- -
Press '1' for option 1: - -
- Amortization Schedule: - Yearly, y, per Payment, p, or Advanced Payment, a, Amortization - Enter choice y, p or a: - <> -- -
Press 'y' for an annual Summary - -
- Amortization Table - Effective Date: Thu Jun 06 00:00:00 1996 - Initial Payment Date: Thu Aug 01 00:00:00 1996 - Compounding Frequency per year: 12 - Payment Frequency per year: 12 - Compounding: Discrete - Payments: End of Period - Payments (179): -1,281.74 - Final payment (# 180): -1,279.73 - Nominal Annual Interest Rate: 13.25 - Effective Interest Rate Per Payment Period: 0.0110417 - Present Value: 100,000.00 - Year Interest Ending Balance - 1996 -5,501.01 -99,092.31 - 1997 -12,987.86 -96,699.29 - 1998 -12,650.80 -93,969.21 - 1999 -12,266.27 -90,854.60 - 2000 -11,827.58 -87,301.30 - 2001 -11,327.09 -83,247.51 - 2002 -10,756.12 -78,622.75 - 2003 -10,104.72 -73,346.59 - 2004 -9,361.57 -67,327.28 - 2005 -8,513.75 -60,460.15 - 2006 -7,546.51 -52,625.78 - 2007 -6,443.04 -43,687.94 - 2008 -5,184.14 -33,491.20 - 2009 -3,747.93 -21,858.25 - 2010 -2,109.42 -8,586.79 - 2011 -383.38 0.00 - - Total Interest: -130,711.19 -- -
The toral interest is reduced to $130,711.19. This compares to: - -
Balloon Payment -
On long term loans, small changes in the periodic payments can generate -large changes in the future value. If the monthly payment in the previous example is -rounded down to $1125, how much additional (balloon) payment will be due -with the final regular payment. -
- <>s - Financial Calculator - Copyright (C) 1990 - 1997 Terry D. Boldt, All Rights Reserved. - Current Financial Calculator Status: - Compounding Frequency: (CF) 12 - Payment Frequency: (PF) 12 - Compounding: Discrete (disc = TRUE) - Payments: End of Period (bep = FALSE) - Number of Payment Periods (n): 180 (Years: 15) - Nominal Annual Interest Rate (i): 13.25 - Effective Interest Rate Per Payment Period: 0.0110417 - Present Value (pv): 100,000.00 - Periodic Payment (pmt): -1,281.74 - Future Value (fv): 0.00 - Effective Date: Thu Jun 06 00:00:00 1996(2450241) - Initial Payment Date: Thu Aug 01 00:00:00 1996(2450297) - <>n=360 - 360 - <>pmt=-1125 - -1,125 - <>FV - -3,579.99 - <> -- - -
Canadian Mortgage -
A "Canadian Mortgage" is defined with semi-annual compunding, CF == 2, -and monthly payments, PF == 12. - -
Find the monthly end-of-period payment necessary to fully amortize a 25 year -$85,000 loan at 11% compounded semi-annually. -
- <>d - <>CF=2 - 2 - <>n=300 - 300 - <>i=11 - 11 - <>pv=85000 - 85,000 - <>PMT - -818.15 -- - - -
European Mortgage -
The "effective annual rate (EAR)" is used in some countries (especially - in Europe) in lieu of the nominal rate commonly used in the United States - and Canada. For a 30 year $90,000 mortgage at 14% (EAR), compute the monthly - end-of-period payments. When using an EAR, the compounding frequency is - set to 1. -
- <>d - <>CF=1 - 1 - <>n=30*12 - 360 - <>i=14 - 14 - <>pv=90000 - 90,000 - <>PMT - -1,007.88 -- - -
Bi-weekly Savings -
Compute the future value, fv, of bi-weekly savings of $100 for 3 years at a - nominal annual rate of 5.5% compounded daily. (Set payment to - beginning-of-period, bep = TRUE) -
- <>d - <>bep=TRUE - 1 - <>CF=365 - 365 - <>PF=26 - 26 - <>n=3*26 - 78 - <>i=5.5 - 5.50 - <>pmt=-100 - -100 - <>FV - 8,489.32 -- - -
Present Value - Annuity Due -
What is the present value of $500 to be received at the beginning of each - quarter over a 10 year period if money is being discounted at 10% nominal - annual rate compounded monthly? -
- <>d - <>bep=TRUE - 1 - <>PF=4 - 4 - <>n=4*10 - 40 - <>i=10 - 10 - <>pmt=500 - 500 - <>PV - -12,822.64 -- - -
Effective Rate - 365/360 Basis -
Compute the effective annual rate (%APR) for a nominal annual rate of 12% - compounded on a 365/360 basis used by some Savings & Loan Associations. -
- <>d - <>n=365 - 365 - <>CF=365 - 365 - <>PF=360 - 360 - <>i=12 - 12 - <>pv=-100 - -100 - <>FV - 112.94 - <>fv+pv - 12.94 -- - -
Certificate of Deposit, Annual Percentage Yield -
Most, if not all banks have started stating return rates on Certificates of Deposit, CDs, as -an Annual Percentage Yoild, APY, and the nominal annual interest. For example, a bank will advertise -a CD with a 18 month term, an APY of 5.20% and a nominal rate of 5.00. What values of CF and PF will -are being used? - -
- <>d - <>n=365 - 365 - <>CF=PF=365 - 365 - <>i=5 - 5 - <>pv=-100 - -100 - <>FV - 105.13 - <>CF=PF=360 - 360 - <>fv+pv - -5.20 -- -
Mortgage with "Points" -
What is the true APR of a 30 year, $75,000 loan at a nominal rate of 13.25% - compounded monthly, with monthly end-of-period payments, if 3 "points" - are charged? The pv must be reduced by the dollar value of the points - and/or any lenders fees to establish an effective pv. Because payments remain - the same, the true APR will be higher than the nominal rate. Note, first - compute the payments on the pv of the loan amount. -
- <>n=30*12 - 360 - <>i=13.25 - 13.25 - <>pv=75000 - 75,000 - <>PMT - -844.33 - <>pv-=pv*0.03 - 72,750.00 - <>I - 13.69 - <> -- - -
Equivalent Payments -
Find the equivalent monthly payment required to amortize a 20 year $40,000 -loan at 10.5% nominal annual rate compounded monthly, with 10 annual -payments of $5029.71 remaining. Compute the pv of the remaining annual -payments, then change n, the number of periods, and the payment frequency, -PF, to a monthly basis and compute the equivalent monthly pmt. -
- <>d - <>PF=1 - 1 - <>n=10 - 10 - <>i=10.5 - 10.50 - <>pmt=-5029.71 - -5,029.71 - <>PV - 29,595.88 - <>PF=12 - 12 - <>n=120 - 120 - <>PMT - -399.35 -- - -
Perpetuity - Continuous Compounding -
If you can purchase a single payment annuity with an initial investment of - $60,000 that will be invested at 15% nominal annual rate compounded - continuously, what is the maximum monthly return you can receive without - reducing the $60,000 principal? If the principal is not disturbed, the - payments can go on indefinitely (a perpetuity). Note that the term,n, of - a perpetuity is immaterial. It can be any non-zero value. -
- <>d - <>disc=FALSE - 0 - <>n=12 - 12 - <>CF=1 - 1 - <>i=15 - 15 - <>fv=60000 - 60,000 - <>pv=-60000 - -60,000 - <>PMT - 754.71 -- - -
Investment Return -
A development company is purchasing an investment property with an annual net cash -flow of $25,000.00. The expected holding period for the property is 10 years with an estimated -selling price of $850,000.00 at that time. If the company is to realize a 15% yield on the -investment, what is the maximum price they can pay for the property today? - -
- Financial Calculator - Copyright (C) 1990 - 1997 Terry D. Boldt, All Rights Reserved. - <>CF=PF=1 - 1 - <>n=10 - 10 - <>i=15 - 15 - <>pmt=25000 - 25,000 - <>fv=850000 - 850,000 - <>PV - -335,576.22 -- -
So the maximum purchase price today would be $335,576.22 to achieve the desired yield.
-
-
-Retirement Investment
-
Retirement Investment -
You wish to retire in 20 years and wish to deposit a lump sum amount in an account -today which will grow to $100,000.00, earning 6.5% interest compounded semi-annually. -How much do you need to deposit? - -
- Financial Calculator - Copyright (C) 1990 - 1997 Terry D. Boldt, All Rights Reserved. - <>CF=PF=2 - 2 - <>n=2*20 - 40 - <>i=6.5 - 6.50 - <>fv=100000 - 100,000 - <>PV - -27,822.59 -- -
If you were to make semi-annual deposits of $600.00, how much would you need to deposit today? - -
- <>pmt=-600 - -600 - <>PV - -14,497.53 -- -
If you were to make monthly deposits of $100.00? - -
- <>PF=12 - 12 - <>n=20*12 - 240 - <>pmt=-100 - -100 - <>PV - -14,318.21 -- - -
Property Values -
Property values in an area you are considering moving to are declining at the rate -of 2.35% annually. What will property presently appraised at $155,500.00 be worth in 10 years -if the trend continues? - -
- Financial Calculator - Copyright (C) 1990 - 1997 Terry D. Boldt, All Rights Reserved. - <>CF=PF=1 - 1 - <>n=10 - 10 - <>i=-2.35 - -2.35 - <>pv=155500 - 155,500 - <>FV - -122,589.39 -- - -
College Expenses -
You and your spouse are planning for your child's college expenses. Your child -will be entering college in 15 years. You expect that college expenses at that time -will amount to $25,000.00 per year or about $2,100.00/month. If the child withdrew -the expenses from a bank account monthly paying 6% compounded on a daily basis (using -360 days/year), how much must you deposit in the account at the start of the four -years? - -
- Financial Calculator - Copyright (C) 1990 - 1997 Terry D. Boldt, All Rights Reserved. - <>CF=360 - 360 - <>PF=12 - 12 - <>n=12*4 - 48 - <>i=6 - 6 - <>pmt=2100 - 2,100 - <>PV - -89,393.32 -- -
Your next problem is how to accumulate the money by the time the child starts college. -You have a $50,000.00 paid-up insurance policy for your child that has a cash value -of $6,500.00. It is accumulating annual dividends of $1,200 earning 6.75% compounded monthly. -What will be the cash value of the policy in 15 years? - -
- <>college_fund=-pv - 89,393.32 - <>d - <>PF=1 - 1 - <>n=20 - 20 - <>i=6.75 - 6.75 - <>pmt=1200 - 1,200 - <>FV - -48,995.19 - <>insurance=-fv+6500 - 55,495.19 - <>college_fund-insurance - 33,898.13 -- -
The paid-up insurance cash value and dividends will provide $55,495.19 of the amount -necessary, leaving $33,898.13 to accumulate in savings. Making monthly payments into -a savings account paying 4.5% compounded daily, what level of monthly payments would be -needed? - -
- Financial Calculator - Copyright (C) 1990 - 1997 Terry D. Boldt, All Rights Reserved. - <>d - <>CF=360 - 360 - <>n=PF*15 - 180 - <>i=4.5 - 4.50 - <>fv=college_fund - insurance - 33,898.13 - <>PMT - -132.11 -- - -