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fpspreadsheet: Add interest rate calculation to complete financial functions supported by fpspreadsheet. Extract financial stuff into separate unit "financemath.pas" which will be proposed as a fpc feature request.

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git-svn-id: https://svn.code.sf.net/p/lazarus-ccr/svn@3294 8e941d3f-bd1b-0410-a28a-d453659cc2b4
This commit is contained in:
wp_xxyyzz 2014-07-07 12:04:33 +00:00
parent c30222aac7
commit 9f226d94bd
4 changed files with 414 additions and 273 deletions
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184
components/fpspreadsheet/examples/other/financemath.pas Normal file
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@ -0,0 +1,184 @@
unit financemath;
{$mode objfpc}{$H+}
interface
uses
Classes, SysUtils;
{ Cash flow equation:
FV + PV * q^n + PMT (q^n - 1) / (q - 1) = 0 (1)
with
q = 1 + interest rate (RATE)
PV = present value of an investment
FV = future value of an investment
PMT = regular payment (per period)
n = NPER = number of payment periods
This is valid for payments occuring at the end of each period. If payments
occur at the start of each period the payments are multiplied by a factor q.
This case is indicated by means of the parameter PaymentTime below.
The interest rate is considered as "per period" - whatever that is.
If the period is 1 year then we use the "usual" interest rate.
If the period is 1 month then we use 1/12 of the yearly interest rate.
Sign rules:
- Money that I receive is to a positive number
- Money that I pay is to a negative number.
Example 1: Saving account
- A saving account has an initial balance of 1000 $ (PV).
I paid this money to the bank --> negative number
- I deposit 100$ regularly to this account (PMT): I pay this money --> negative number.
- At the end of the payments (NPER periods) I get the money back --> positive number.
This is the FV.
Example 2: Loan
- I borrow 1000$ from the bank: I get money --> positive PV
- I pay 100$ back to the bank in regular intervals --> negative PMT
- At the end, all debts are paid --> FV = 0.
The cash flow equation (1) contains 5 parameters (Rate, PV, FV, PMT, NPER).
The functions below solve this equation always for one of these parameters.
References:
- http://en.wikipedia.org/wiki/Time_value_of_money
- https://wiki.openoffice.org/wiki/Documentation/How_Tos/Calc:_Derivation_of_Financial_Formulas
}
type
TPaymentTime = (ptEndOfPeriod, ptStartOfPeriod);
function FutureValue(ARate: Extended; NPeriods: Integer;
APayment, APresentValue: Extended; APaymentTime: TPaymentTime): Extended;
function InterestRate(NPeriods: Integer; APayment, APresentValue, AFutureValue: Extended;
APaymentTime: TPaymentTime): Extended;
function NumberOfPeriods(ARate, APayment, APresentValue, AFutureValue: Extended;
APaymentTime: TPaymentTime): Extended;
function Payment(ARate: Extended; NPeriods: Integer;
APresentValue, AFutureValue: Extended; APaymentTime: TPaymentTime): Extended;
function PresentValue(ARate: Extended; NPeriods: Integer;
APayment, AFutureValue: Extended; APaymentTime: TPaymentTime): Extended;
implementation
uses
math;
function FutureValue(ARate: Extended; NPeriods: Integer;
APayment, APresentValue: Extended; APaymentTime: TPaymentTime): Extended;
var
q, qn, factor: Extended;
begin
if ARate = 0 then
Result := -APresentValue - APayment * NPeriods
else begin
q := 1.0 + ARate;
qn := power(q, NPeriods);
factor := (qn - 1) / (q - 1);
if APaymentTime = ptStartOfPeriod then
factor := factor * q;
Result := -(APresentValue * qn + APayment*factor);
end;
end;
function InterestRate(NPeriods: Integer; APayment, APresentValue, AFutureValue: Extended;
APaymentTime: TPaymentTime): Extended;
{ The interest rate cannot be calculated analytically. We solve the equation
numerically by means of the Newton method:
- guess value for the interest reate
- calculate at which interest rate the tangent of the curve fv(rate)
(straight line!) has the requested future vale.
- use this rate for the next iteration. }
const
DELTA = 0.001;
EPS = 1E-9; // required precision of interest rate (after typ. 6 iterations)
MAXIT = 20; // max iteration count to protect agains non-convergence
var
r1, r2, dr: Extended;
fv1, fv2: Extended;
iteration: Integer;
begin
iteration := 0;
r1 := 0.05; // inital guess
repeat
r2 := r1 + DELTA;
fv1 := FutureValue(r1, NPeriods, APayment, APresentValue, APaymentTime);
fv2 := FutureValue(r2, NPeriods, APayment, APresentValue, APaymentTime);
dr := (AFutureValue - fv1) / (fv2 - fv1) * delta; // tangent at fv(r)
r1 := r1 + dr; // next guess
inc(iteration);
until (abs(dr) < EPS) or (iteration >= MAXIT);
Result := r1;
end;
function NumberOfPeriods(ARate, APayment, APresentValue, AFutureValue: extended;
APaymentTime: TPaymentTime): extended;
{ Solve the cash flow equation (1) for q^n and take the logarithm }
var
q, x1, x2: Extended;
begin
if ARate = 0 then
Result := -(APresentValue + AFutureValue) / APayment
else begin
q := 1.0 + ARate;
if APaymentTime = ptStartOfPeriod then
APayment := APayment * q;
x1 := APayment - AFutureValue * ARate;
x2 := APayment + APresentValue * ARate;
if (x2 = 0) // we have to divide by x2
or (sign(x1) * sign(x2) < 0) // the argument of the log is negative
then
Result := Infinity
else begin
Result := ln(x1/x2) / ln(q);
end;
end;
end;
function Payment(ARate: Extended; NPeriods: Integer;
APresentValue, AFutureValue: Extended; APaymentTime: TPaymentTime): Extended;
var
q, qn, factor: Extended;
begin
if ARate = 0 then
Result := -(AFutureValue + APresentValue) / NPeriods
else begin
q := 1.0 + ARate;
qn := power(q, NPeriods);
factor := (qn - 1) / (q - 1);
if APaymentTime = ptStartOfPeriod then
factor := factor * q;
Result := -(AFutureValue + APresentValue * qn) / factor;
end;
end;
function PresentValue(ARate: Extended; NPeriods: Integer;
APayment, AFutureValue: Extended; APaymentTime: TPaymentTime): Extended;
var
q, qn, factor: Extended;
begin
if ARate = 0.0 then
Result := -AFutureValue - APayment * NPeriods
else begin
q := 1.0 + ARate;
qn := power(q, NPeriods);
factor := (qn - 1) / (q - 1);
if APaymentTime = ptStartOfPeriod then
factor := factor * q;
Result := -(AFutureValue + APayment*factor) / qn;
end;
end;
end.

7
components/fpspreadsheet/examples/other/test_formula_func.lpi
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@ -60,12 +60,17 @@
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123
components/fpspreadsheet/examples/other/test_formula_func.lps
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@ -4,204 +4,211 @@
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373
components/fpspreadsheet/examples/other/test_formula_func.pas
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@ -24,134 +24,29 @@ uses
{$ENDIF}{$ENDIF}
Classes, SysUtils, laz_fpspreadsheet
{ you can add units after this },
math, fpspreadsheet, xlsbiff8, fpsfunc;
math, fpspreadsheet, xlsbiff8, fpsfunc, financemath;
{------------------------------------------------------------------------------}
{ Basic implmentation of the four financial funtions }
{------------------------------------------------------------------------------}
const
paymentAtEnd = 0;
paymentAtBegin = 1;
{ Calculates the future value (FV) of an investment based on an interest rate and
a constant payment schedule:
- "interest_rate" (r) is the interest rate for the investment (as decimal, not percent)
- "number_periods" (n) is the number of payment periods, i.e. number of payments
for the annuity.
- "payment" (PMT) is the amount of the payment made each period
- "pv" is the present value of the payments.
- "payment_type" indicates when the payments are due (see paymentAtXXX constants)
see: http://en.wikipedia.org/wiki/Time_value_of_money
or https://wiki.openoffice.org/wiki/Documentation/How_Tos/Calc:_Derivation_of_Financial_Formulas#PV.2C_FV.2C_PMT.2C_NPER.2C_RATE
As in Excel's implementation the cash flow is a signed number:
- Positive cash flow means: "I get money"
- Negative cash flow means: "I pay money"
With these conventions, the contributions (FV, PV, Payments) add up to 0:
FV + PV q^n + PMT (q^n - 1) / (q - 1) = 0 ( q = 1 + r )
}
function FV(interest_rate: Double; number_periods: Integer; payment, pv: Double;
payment_type: integer): Double;
var
q, qn, factor: Double;
begin
q := 1.0 + interest_rate;
qn := power(q, number_periods);
factor := (qn - 1) / (q - 1);
if payment_type = paymentAtBegin then
factor := factor * q;
Result := -(pv * qn + payment*factor);
end;
{ Calculates the number of periods for an investment based on an interest rate
and a constant payment schedule.
Solve above formula for qn and then take the log to get n.
}
function NPER(interest_rate, payment, pv, fv: Double;
payment_type:Integer): double;
var
q, x1, x2, T: Double;
begin
if interest_rate = 0 then
Result := (pv + fv) / payment
else
q := 1.0 + interest_rate;
if payment_type = paymentAtBegin then
payment := payment * q;
x2 := pv * interest_rate + payment;
if x2 = 0 then
Result := Infinity
else begin
x1 := -fv * interest_rate + payment;
Result := ln(x1/x2) / ln(q);
end;
end;
{ Calculates the regular payments for a loan based on an interest rate and a
constant payment schedule
Arguments as shown for FV(), in addition:
- "fv" is the future value of the payments.
see: http://en.wikipedia.org/wiki/Time_value_of_money
}
function PMT(interest_rate: Double; number_periods: Integer; pv, fv: Double;
payment_type: Integer): Double;
var
q, qn, factor: Double;
begin
q := 1.0 + interest_rate;
qn := power(q, number_periods);
factor := (qn - 1) / (q - 1);
if payment_type = paymentAtBegin then
factor := factor * q;
Result := -(fv + pv * qn) / factor;
end;
{ Calculates the present value of an investment based on an interest rate and
a constant payment schedule.
Arguments as shown for FV(), in addition:
- "fv" is the future value of the payments.
see: http://en.wikipedia.org/wiki/Time_value_of_money
}
function PV(interest_rate: Double; number_periods: Integer; payment, fv: Double;
payment_type: Integer): Double;
var
q, qn, factor: Double;
begin
q := 1.0 + interest_rate;
qn := power(q, number_periods);
factor := (qn - 1) / (q - 1);
if payment_type = paymentAtBegin then
factor := factor * q;
Result := -(fv + payment*factor) / qn;
end;
{------------------------------------------------------------------------------}
{ Adaption for usage by fpspreadsheet }
{ Adaption of financial functions to usage by fpspreadsheet }
{ The functions are implemented in the unit "financemath.pas". }
{------------------------------------------------------------------------------}
function fpsFV(Args: TsArgumentStack; NumArgs: Integer): TsArgument;
var
data: TsArgNumberArray;
begin
// Pop the argument off the stack. This can be done by means of PopNumberValues
// which brings the values back into the right order and reports an error
// Pop the argument from the stack. This can be done by means of PopNumberValues
// which brings the values back in the right order and reports an error
// in case of non-numerical values.
if Args.PopNumberValues(NumArgs, false, data, Result) then
// Call our FV function with the NumberValues of the arguments.
Result := CreateNumberArg(FV(
// Call the FutureValue function with the NumberValues of the arguments.
Result := CreateNumberArg(FutureValue(
data[0], // interest rate
round(data[1]), // number of payments
data[2], // payment
data[3], // present value
round(data[4]) // payment type
TPaymentTime(round(data[4])) // payment type
));
end;
@ -160,12 +55,12 @@ var
data: TsArgNumberArray;
begin
if Args.PopNumberValues(NumArgs, false, data, Result) then
Result := CreateNumberArg(PMT(
Result := CreateNumberArg(Payment(
data[0], // interest rate
round(data[1]), // number of payments
data[2], // present value
data[3], // future value
round(data[4]) // payment type
TPaymentTime(round(data[4])) // payment type
));
end;
@ -174,12 +69,12 @@ var
data: TsArgNumberArray;
begin
if Args.PopNumberValues(NumArgs, false, data, Result) then
Result := CreateNumberArg(PV(
Result := CreateNumberArg(PresentValue(
data[0], // interest rate
round(data[1]), // number of payments
data[2], // payment
data[3], // future value
round(data[4]) // payment type
TPaymentTime(round(data[4])) // payment type
));
end;
@ -188,12 +83,26 @@ var
data: TsArgNumberArray;
begin
if Args.PopNumberValues(NumArgs, false, data, Result) then
Result := CreateNumberArg(NPER(
Result := CreateNumberArg(NumberOfPeriods(
data[0], // interest rate
data[1], // payment
data[2], // present value
data[3], // future value
round(data[4]) // payment type
TPaymentTime(round(data[4])) // payment type
));
end;
function fpsRATE(Args: TsArgumentStack; NumArgs: Integer): TsArgument;
var
data: TsArgNumberArray;
begin
if Args.PopNumberValues(NumArgs, false, data, Result) then
Result := CreateNumberArg(InterestRate(
round(data[0]), // number of payment periods
data[1], // payment
data[2], // present value
data[3], // future value
TPaymentTime(round(data[4])) // payment type
));
end;
@ -202,159 +111,192 @@ end;
{------------------------------------------------------------------------------}
procedure WriteFile(AFileName: String);
const
INTEREST_RATE = 0.03;
NUMBER_PAYMENTS = 10;
PAYMENT = 1000;
PRESENT_VALUE = 10000;
PAYMENT_WHEN = paymentAtEnd;
INTEREST_RATE = 0.03; // interest rate per period
NUMBER_PAYMENTS = 10; // number of payment periods
REG_PAYMENT = 1000; // regular payment per period
PRESENT_VALUE = 10000; // present value of investment
PAYMENT_WHEN: TPaymentTime = ptEndOfPeriod; // when is the payment made
var
workbook: TsWorkbook;
worksheet: TsWorksheet;
fval, pval, pmtval, nperval: Double;
fval, pval, pmtval, nperval, rateval: Double;
begin
{ We have to register our financial function in fpspreadsheet. Otherwise an
error code would be displayed in the reading part of this demo in these
{ We have to register our financial functions in fpspreadsheet. Otherwise an
error code would be displayed in the reading part of this demo for these
formula cells. }
RegisterFormulaFunc(fekFV, @fpsFV);
RegisterFormulaFunc(fekPMT, @fpsPMT);
RegisterFormulaFunc(fekPV, @fpsPV);
RegisterFormulaFunc(fekNPER, @fpsNPER);
RegisterFormulaFunc(fekRATE, @fpsRATE);
workbook := TsWorkbook.Create;
try
worksheet := workbook.AddWorksheet('Financial');
worksheet.Options := worksheet.Options + [soCalcBeforeSaving];
worksheet.WriteColWidth(0, 40);
worksheet.WriteColWidth(1, 15);
worksheet.WriteUTF8Text(0, 0, 'Interest rate');
worksheet.WriteNumber(0, 1, INTEREST_RATE, nfPercentage, 1); // B1
worksheet.WriteUTF8Text(0, 0, 'INPUT DATA');
worksheet.WriteFontStyle(0, 0, [fssBold]);
worksheet.WriteUTF8Text(1, 0, 'Number of payments');
worksheet.WriteNumber(1, 1, NUMBER_PAYMENTS); // B2
worksheet.WriteUTF8Text(1, 0, 'Interest rate');
worksheet.WriteNumber(1, 1, INTEREST_RATE, nfPercentage, 1); // B2
worksheet.WriteUTF8Text(2, 0, 'Payment');
worksheet.WriteCurrency(2, 1, PAYMENT, nfCurrency, 2, '$'); // B3
worksheet.WriteUTF8Text(2, 0, 'Number of payments');
worksheet.WriteNumber(2, 1, NUMBER_PAYMENTS); // B3
worksheet.WriteUTF8Text(3, 0, 'Present value');
worksheet.WriteCurrency(3, 1, PRESENT_VALUE, nfCurrency, 2, '$'); // B4
worksheet.WriteUTF8Text(3, 0, 'Payment');
worksheet.WriteCurrency(3, 1, REG_PAYMENT, nfCurrency, 2, '$'); // B4
worksheet.WriteUTF8Text(4, 0, 'Payment at end (0) or at begin (1)');
worksheet.WriteNumber(4, 1, PAYMENT_WHEN); // B5
worksheet.WriteUTF8Text(4, 0, 'Present value');
worksheet.WriteCurrency(4, 1, PRESENT_VALUE, nfCurrency, 2, '$'); // B5
worksheet.WriteUTF8Text(5, 0, 'Payment at end (0) or at begin (1)');
worksheet.WriteNumber(5, 1, ord(PAYMENT_WHEN)); // B6
// future value calculation
fval := FV(INTEREST_RATE, NUMBER_PAYMENTS, PAYMENT, PRESENT_VALUE, PAYMENT_WHEN);
worksheet.WriteUTF8Text(6, 0, 'Calculation of the future value');
worksheet.WriteFontStyle(6, 0, [fssBold]);
worksheet.WriteUTF8Text(7, 0, 'Our calculation');
worksheet.WriteCurrency(7, 1, fval, nfCurrency, 2, '$');
fval := FutureValue(INTEREST_RATE, NUMBER_PAYMENTS, REG_PAYMENT, PRESENT_VALUE, PAYMENT_WHEN);
worksheet.WriteUTF8Text(7, 0, 'CALCULATION OF THE FUTURE VALUE');
worksheet.WriteFontStyle(7, 0, [fssBold]);
worksheet.WriteUTF8Text(8, 0, 'Direct calculation');
worksheet.WriteCurrency(8, 1, fval, nfCurrency, 2, '$');
worksheet.WriteUTF8Text(8, 0, 'Excel''s calculation using constants');
worksheet.WriteNumberFormat(8, 1, nfCurrency, 2, '$');
worksheet.WriteRPNFormula(8, 1, CreateRPNFormula( // B9
worksheet.WriteUTF8Text(9, 0, 'Worksheet calculation using constants');
worksheet.WriteNumberFormat(9, 1, nfCurrency, 2, '$');
worksheet.WriteRPNFormula(9, 1, CreateRPNFormula(
RPNNumber(INTEREST_RATE,
RPNNumber(NUMBER_PAYMENTS,
RPNNumber(PAYMENT,
RPNNumber(REG_PAYMENT,
RPNNumber(PRESENT_VALUE,
RPNNumber(PAYMENT_WHEN,
RPNNumber(ord(PAYMENT_WHEN),
RPNFunc(fekFV, 5,
nil))))))));
worksheet.WriteUTF8Text(9, 0, 'Excel''s calculation using cell values');
worksheet.WriteNumberFormat(9, 1, nfCurrency, 2, '$');
worksheet.WriteRPNFormula(9, 1, CreateRPNFormula( // B9
RPNCellValue('B1', // interest rate
RPNCellValue('B2', // number of periods
RPNCellValue('B3', // payment
RPNCellValue('B4', // present value
RPNCellValue('B5', // payment at end or at start
worksheet.WriteUTF8Text(10, 0, 'Worksheet calculation using cell values');
worksheet.WriteNumberFormat(10, 1, nfCurrency, 2, '$');
worksheet.WriteRPNFormula(10, 1, CreateRPNFormula(
RPNCellValue('B2', // interest rate
RPNCellValue('B3', // number of periods
RPNCellValue('B4', // payment
RPNCellValue('B5', // present value
RPNCellValue('B6', // payment at end or at start
RPNFunc(fekFV, 5, // Call Excel's FV formula
nil))))))));
// present value calculation
pval := PV(INTEREST_RATE, NUMBER_PAYMENTS, PAYMENT, fval, PAYMENT_WHEN);
worksheet.WriteUTF8Text(11, 0, 'Calculation of the present value');
worksheet.WriteFontStyle(11, 0, [fssBold]);
worksheet.WriteUTF8Text(12, 0, 'Our calculation');
worksheet.WriteCurrency(12, 1, pval, nfCurrency, 2, '$');
pval := PresentValue(INTEREST_RATE, NUMBER_PAYMENTS, REG_PAYMENT, fval, PAYMENT_WHEN);
worksheet.WriteUTF8Text(12, 0, 'CALCULATION OF THE PRESENT VALUE');
worksheet.WriteFontStyle(12, 0, [fssBold]);
worksheet.WriteUTF8Text(13, 0, 'Direct calculation');
worksheet.WriteCurrency(13, 1, pval, nfCurrency, 2, '$');
worksheet.WriteUTF8Text(13, 0, 'Excel''s calculation using constants');
worksheet.WriteNumberFormat(13, 1, nfCurrency, 2, '$');
worksheet.WriteRPNFormula(13, 1, CreateRPNFormula(
RPNNumber(INTEREST_RATE,
RPNNumber(NUMBER_PAYMENTS,
RPNNumber(PAYMENT,
RPNNumber(fval,
RPNNumber(PAYMENT_WHEN,
RPNFunc(fekPV, 5,
nil))))))));
Worksheet.WriteUTF8Text(14, 0, 'Excel''s calculation using cell values');
worksheet.WriteUTF8Text(14, 0, 'Worksheet calculation using constants');
worksheet.WriteNumberFormat(14, 1, nfCurrency, 2, '$');
worksheet.WriteRPNFormula(14, 1, CreateRPNFormula(
RPNCellValue('B1', // interest rate
RPNCellValue('B2', // number of periods
RPNCellValue('B3', // payment
RPNCellValue('B10', // future value
RPNCellValue('B5', // payment at end or at start
RPNNumber(INTEREST_RATE,
RPNNumber(NUMBER_PAYMENTS,
RPNNumber(REG_PAYMENT,
RPNNumber(fval,
RPNNumber(ord(PAYMENT_WHEN),
RPNFunc(fekPV, 5,
nil))))))));
Worksheet.WriteUTF8Text(15, 0, 'Worksheet calculation using cell values');
worksheet.WriteNumberFormat(15, 1, nfCurrency, 2, '$');
worksheet.WriteRPNFormula(15, 1, CreateRPNFormula(
RPNCellValue('B2', // interest rate
RPNCellValue('B3', // number of periods
RPNCellValue('B4', // payment
RPNCellValue('B11', // future value
RPNCellValue('B6', // payment at end or at start
RPNFunc(fekPV, 5, // Call Excel's PV formula
nil))))))));
// payments calculation
pmtval := PMT(INTEREST_RATE, NUMBER_PAYMENTS, PRESENT_VALUE, fval, PAYMENT_WHEN);
worksheet.WriteUTF8Text(16, 0, 'Calculation of the payment');
worksheet.WriteFontStyle(16, 0, [fssBold]);
worksheet.WriteUTF8Text(17, 0, 'Our calculation');
worksheet.WriteCurrency(17, 1, pmtval, nfCurrency, 2, '$');
pmtval := Payment(INTEREST_RATE, NUMBER_PAYMENTS, PRESENT_VALUE, fval, PAYMENT_WHEN);
worksheet.WriteUTF8Text(17, 0, 'CALCULATION OF THE PAYMENT');
worksheet.WriteFontStyle(17, 0, [fssBold]);
worksheet.WriteUTF8Text(18, 0, 'Direct calculation');
worksheet.WriteCurrency(18, 1, pmtval, nfCurrency, 2, '$');
worksheet.WriteUTF8Text(18, 0, 'Excel''s calculation using constants');
worksheet.WriteNumberFormat(18, 1, nfCurrency, 2, '$');
worksheet.WriteRPNFormula(18, 1, CreateRPNFormula(
worksheet.WriteUTF8Text(19, 0, 'Worksheet calculation using constants');
worksheet.WriteNumberFormat(19, 1, nfCurrency, 2, '$');
worksheet.WriteRPNFormula(19, 1, CreateRPNFormula(
RPNNumber(INTEREST_RATE,
RPNNumber(NUMBER_PAYMENTS,
RPNNumber(PRESENT_VALUE,
RPNNumber(fval,
RPNNumber(PAYMENT_WHEN,
RPNNumber(ord(PAYMENT_WHEN),
RPNFunc(fekPMT, 5,
nil))))))));
Worksheet.WriteUTF8Text(19, 0, 'Excel''s calculation using cell values');
worksheet.WriteNumberFormat(19, 1, nfCurrency, 2, '$');
worksheet.WriteRPNFormula(19, 1, CreateRPNFormula(
RPNCellValue('B1', // interest rate
RPNCellValue('B2', // number of periods
RPNCellValue('B4', // present value
RPNCellValue('B10', // future value
RPNCellValue('B5', // payment at end or at start
Worksheet.WriteUTF8Text(20, 0, 'Worksheet calculation using cell values');
worksheet.WriteNumberFormat(20, 1, nfCurrency, 2, '$');
worksheet.WriteRPNFormula(20, 1, CreateRPNFormula(
RPNCellValue('B2', // interest rate
RPNCellValue('B3', // number of periods
RPNCellValue('B5', // present value
RPNCellValue('B11', // future value
RPNCellValue('B6', // payment at end or at start
RPNFunc(fekPMT, 5, // Call Excel's PMT formula
nil))))))));
// number of periods calculation
nperval := NPER(INTEREST_RATE, PAYMENT, PRESENT_VALUE, fval, PAYMENT_WHEN);
worksheet.WriteUTF8Text(21, 0, 'Calculation of the number of payment periods');
worksheet.WriteFontStyle(21, 0, [fssBold]);
worksheet.WriteUTF8Text(22, 0, 'Our calculation');
worksheet.WriteNumber(22, 1, nperval, nfFixed, 2);
nperval := NumberOfPeriods(INTEREST_RATE, REG_PAYMENT, PRESENT_VALUE, fval, PAYMENT_WHEN);
worksheet.WriteUTF8Text(22, 0, 'CALCULATION OF THE NUMBER OF PAYMENT PERIODS');
worksheet.WriteFontStyle(22, 0, [fssBold]);
worksheet.WriteUTF8Text(23, 0, 'Direct calculation');
worksheet.WriteNumber(23, 1, nperval, nfFixed, 2);
worksheet.WriteUTF8Text(23, 0, 'Excel''s calculation using constants');
worksheet.WriteNumberFormat(23, 1, nfFixed, 2);
worksheet.WriteRPNFormula(23, 1, CreateRPNFormula(
RPNNumber(INTEREST_RATE,
RPNNumber(PAYMENT,
RPNNumber(PRESENT_VALUE,
RPNNumber(fval,
RPNNumber(PAYMENT_WHEN,
RPNFunc(fekNPER, 5,
nil))))))));
Worksheet.WriteUTF8Text(24, 0, 'Excel''s calculation using cell values');
worksheet.WriteUTF8Text(24, 0, 'Worksheet calculation using constants');
worksheet.WriteNumberFormat(24, 1, nfFixed, 2);
worksheet.WriteRPNFormula(24, 1, CreateRPNFormula(
RPNCellValue('B1', // interest rate
RPNCellValue('B3', // payment
RPNCellValue('B4', // present value
RPNCellValue('B10', // future value
RPNCellValue('B5', // payment at end or at start
RPNNumber(INTEREST_RATE,
RPNNumber(REG_PAYMENT,
RPNNumber(PRESENT_VALUE,
RPNNumber(fval,
RPNNumber(ord(PAYMENT_WHEN),
RPNFunc(fekNPER, 5,
nil))))))));
Worksheet.WriteUTF8Text(25, 0, 'Worksheet calculation using cell values');
worksheet.WriteNumberFormat(25, 1, nfFixed, 2);
worksheet.WriteRPNFormula(25, 1, CreateRPNFormula(
RPNCellValue('B2', // interest rate
RPNCellValue('B4', // payment
RPNCellValue('B5', // present value
RPNCellValue('B11', // future value
RPNCellValue('B6', // payment at end or at start
RPNFunc(fekNPER, 5, // Call Excel's PMT formula
nil))))))));
// interest rate calculation
rateval := InterestRate(NUMBER_PAYMENTS, REG_PAYMENT, PRESENT_VALUE, fval, PAYMENT_WHEN);
worksheet.WriteUTF8Text(27, 0, 'CALCULATION OF THE INTEREST RATE');
worksheet.WriteFontStyle(27, 0, [fssBold]);
worksheet.WriteUTF8Text(28, 0, 'Direct calculation');
worksheet.WriteNumber(28, 1, rateval, nfPercentage, 2);
worksheet.WriteUTF8Text(29, 0, 'Worksheet calculation using constants');
worksheet.WriteNumberFormat(29, 1, nfPercentage, 2);
worksheet.WriteRPNFormula(29, 1, CreateRPNFormula(
RPNNumber(NUMBER_PAYMENTS,
RPNNumber(REG_PAYMENT,
RPNNumber(PRESENT_VALUE,
RPNNumber(fval,
RPNNumber(ord(PAYMENT_WHEN),
RPNFunc(fekRATE, 5,
nil))))))));
Worksheet.WriteUTF8Text(30, 0, 'Worksheet calculation using cell values');
worksheet.WriteNumberFormat(30, 1, nfPercentage, 2);
worksheet.WriteRPNFormula(30, 1, CreateRPNFormula(
RPNCellValue('B3', // number of payments
RPNCellValue('B4', // payment
RPNCellValue('B5', // present value
RPNCellValue('B11', // future value
RPNCellValue('B6', // payment at end or at start
RPNFunc(fekRATE, 5, // Call Excel's PMT formula
nil))))))));
workbook.WriteToFile(AFileName, sfExcel8, true);
finally
@ -389,6 +331,9 @@ begin
s2 := UTF8ToAnsi(worksheet.ReadAsUTF8Text(r, 1));
if s1 = '' then
WriteLn
else
if s2 = '' then
WriteLn(s1)
else
WriteLn(s1+': ':50, s2);
end;