CodeCogs

Enumation of Payment point

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Interface

#include <codecogs/finance/banking/nperiods.h>

using namespace Finance::Banking;

double nPeriods(double rate, double pmtValue, double presentValue, double futureValue, Finance::Banking::PaymentPoint type=pp_EndOfPeriod)

Overview

This enumerate type describes the payment points, which can either occur at the begining or end of each periond, i.e

pp_EndOfPeriod
pp_StartOfPeriod

FUNCTION

nPeriods

Calculates the number of periods for an investment based on periodic, constant payments and a constant interest rate. The function works using the following equation:

$\begin{array}{l}pv*(1.0+rate)^{nper}+ \\ pmt(1.0 + rate*type)* \left ( \frac{(1.0 + rate)^{nper}-1}{rate} \right ) + fv = 0 \end{array}$

(1)

Rearranged to give:

$(1.0+rate)^{nper} = \frac{-fv + pmt(1.0 + rate*type)} {pv + pmt(1.0 + rate*type)}$

(2)

where:

nper is the value we are trying to calculate, the number of periods,
fv is the future value of the investment,
pv is the present value of the investment,
pmt is the payment made each period.

Example 1

#include <iostream>
#include <codecogs/finance/banking/nperiods.h>	
	
int main(void)
{
	printf("nPeriods(0.01, -100, -1000, 10000, pp_StartOfPeriod) = %lf\n",
				 Finance::Banking::nPeriods(0.01,
				-100, -1000, 10000, Finance::Banking::pp_StartOfPeriod));
	
	printf("nPeriods(0.01, -100, -1000, 10000, pp_EndOfPeriod) = %lf\n",
				 Finance::Banking::nPeriods(0.01,
				-100, -1000, 10000, Finance::Banking::pp_EndOfPeriod));
	
	printf("nPeriods(0.01, -100, 1000, 0, pp_EndOfPeriod) = %lf\n",
				 Finance::Banking::nPeriods(0.01,
				-100, 1000, 0,	Finance::Banking::pp_EndOfPeriod));
	
	return 1;
}

Output:

nPeriods(0.01, -100, -1000, 10000, pp_StartOfPeriod) = 59.673866
nPeriods(0.01, -100, -1000, 10000, pp_EndOfPeriod) = 60.082123
nPeriods(0.01, -100, 1000, 0, pp_EndOfPeriod) = 10.588644

Parameters

rate

The interest rate per period of the investment.

pmtValue

The payment made each period. This value must remain

Blank

constant over the life of the annuity.

Parameters

presentValue

The present value of the investment, or the lump-sum

Blank

amount that a series of future payments is worth right now.

Parameters

futureValue

The future value of the investment.

type

A value indicating whether the payment is made at the

Blank

beginning or the end of each period. It is set to either: pp_EndOfPeriod or pp_StartOfPeriod.

Returns

The number of periods of the investment.

Author

James Warren (August 2005)