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fpspreadsheet: Add formula financial function NPER to user-defined formula demo.

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git-svn-id: https://svn.code.sf.net/p/lazarus-ccr/svn@3291 8e941d3f-bd1b-0410-a28a-d453659cc2b4
This commit is contained in:
wp_xxyyzz
2014-07-06 19:13:05 +00:00
parent 486e6b630c
commit 803c910ac6
2 changed files with 158 additions and 75 deletions
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128
components/fpspreadsheet/examples/other/test_formula_func.lps
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@ -4,194 +4,204 @@
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105
components/fpspreadsheet/examples/other/test_formula_func.pas
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@ -3,9 +3,10 @@
calculation procedure.
The example will show implementation of the some financial formulas:
- FV(...) (future value)
- PV(...) (present value)
- PMT(...) (payment)
- FV() (future value)
- PV() (present value)
- PMT() (payment)
- NPER() (number of payment periods)
The demo writes an xls file which uses these formulas and then displays
the result in a console window. (Open the generated file in Excel or
@ -27,25 +28,31 @@ uses
{------------------------------------------------------------------------------}
{ Basic implmentation of the three financial funtions }
{ Basic implmentation of the four financial funtions }
{------------------------------------------------------------------------------}
const
paymentAtEnd = 0;
paymentAtBegin = 1;
{ Calculates the future value of an investment based on an interest rate and
{ Calculates the future value (FV) of an investment based on an interest rate and
a constant payment schedule:
- "interest_rate" is the interest rate for the investment (as decimal, not percent)
- "number_periods" is the number of payment periods, i.e. number of payments
- "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" is the amount of the payment made each period
- "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
In Excel's implementation the payments and the FV add up to 0:
FV + PV q^n + PMT (q^n - 1) / (q - 1) = 0
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;
@ -61,6 +68,30 @@ begin
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:
@ -152,6 +183,19 @@ begin
));
end;
function fpsNPER(Args: TsArgumentStack; NumArgs: Integer): TsArgument;
var
data: TsArgNumberArray;
begin
if Args.PopNumberValues(NumArgs, false, data, Result) then
Result := CreateNumberArg(NPER(
data[0], // interest rate
data[1], // payment
data[2], // present value
data[3], // future value
round(data[4]) // payment type
));
end;
{------------------------------------------------------------------------------}
{ Write xls file comparing our own calculations with Excel result }
@ -167,7 +211,7 @@ const
var
workbook: TsWorkbook;
worksheet: TsWorksheet;
fval, pval, pmtval: Double;
fval, pval, pmtval, nperval: Double;
begin
{ We have to register our financial function in fpspreadsheet. Otherwise an
@ -176,6 +220,7 @@ begin
RegisterFormulaFunc(fekFV, @fpsFV);
RegisterFormulaFunc(fekPMT, @fpsPMT);
RegisterFormulaFunc(fekPV, @fpsPV);
RegisterFormulaFunc(fekNPER, @fpsNPER);
workbook := TsWorkbook.Create;
try
@ -200,7 +245,7 @@ begin
// future value calculation
fval := FV(INTEREST_RATE, NUMBER_PAYMENTS, PAYMENT, PRESENT_VALUE, PAYMENT_WHEN);
worksheet.WriteUTF8Text(6, 0, 'Future value');
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, '$');
@ -228,7 +273,7 @@ begin
// present value calculation
pval := PV(INTEREST_RATE, NUMBER_PAYMENTS, PAYMENT, fval, PAYMENT_WHEN);
worksheet.WriteUTF8Text(11, 0, 'Present value');
worksheet.WriteUTF8Text(11, 0, 'Calculation of the present value');
worksheet.WriteFontStyle(11, 0, [fssBold]);
worksheet.WriteUTF8Text(12, 0, 'Our calculation');
worksheet.WriteCurrency(12, 1, pval, nfCurrency, 2, '$');
@ -256,7 +301,7 @@ begin
// payments calculation
pmtval := PMT(INTEREST_RATE, NUMBER_PAYMENTS, PRESENT_VALUE, fval, PAYMENT_WHEN);
worksheet.WriteUTF8Text(16, 0, 'Payment');
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, '$');
@ -282,6 +327,34 @@ begin
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);
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.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
RPNFunc(fekNPER, 5, // Call Excel's PMT formula
nil))))))));
workbook.WriteToFile(AFileName, sfExcel8, true);
finally
@ -308,7 +381,7 @@ begin
// Write all cells with contents to the console
WriteLn('');
WriteLn('Contents of the first worksheet of the file:');
WriteLn('Contents of file "', AFileName, '"');
WriteLn('');
for r := 0 to worksheet.GetLastRowIndex do begin