interest_rate_annuity

Evaluates the interest rate per period of an annuity.

Synopsis

#include <imsl.h>

float imsl_f_interest_rate_annuity (int n_periods, float payment, float present_value, float future_value, int when, …, 0)

The type double function is imsl_d_interest_rate_annuity.

Required Arguments

int n_periods (Input)
Total number of periods.

float payment (Input)
Payment made each period.

float present_value (Input)
The current value of a stream of future payments, after discounting the payments using some interest rate.

float future_value (Input)
The value, at some time in the future, of a current amount and a stream of payments.

int when (Input)
Time in each period when the payment is made, either IMSL_AT_END_OF_PERIOD or IMSL_AT_BEGINNING_OF_PERIOD. For a more detailed discussion on when see the Usage Notes section of this chapter.

Return Value

The interest rate per period of an annuity. If no result can be computed, NaN is returned.

Synopsis with Optional Arguments

#include <imsl.h>

float imsl_f_interest_rate_annuity (int n_periods, float payment, float present_value, float future_value, int when,
IMSL_XGUESS, float guess,
IMSL_HIGHEST, float max,
0)

Optional Arguments

IMSL_XGUESS, float guess (Input)
Initial guess at the interest rate.

IMSL_HIGHEST, float max (Input)
Maximum value of the interest rate allowed.
Default: 1.0 (100%)

Description

Function imsl_f_interest_rate_annuity computes the interest rate per period of an annuity. An annuity is a security that pays a fixed amount at equally spaced intervals.

It can be found by solving the following:

If rate =0

 

If rate ≠ 0

 

Example

In this example, imsl_f_interest_rate_annuity computes the interest rate of a $20,000 loan that requires 70 payments of $350 each to pay off.

#include <stdio.h>

#include <imsl.h>

 

int main()

{

float rate;

int n_periods = 70;

float payment = -350.;

float present_value = 20000;

float future_value = 0.;

int when = IMSL_AT_BEGINNING_OF_PERIOD;

 

rate = imsl_f_interest_rate_annuity (n_periods, payment, present_value,

future_value, when, 0) * 12;

printf ("The computed interest rate on the loan is ");

printf ("%.2f%%.\n", rate * 100.);

}

Output

The computed interest rate on the loan is 7.35%.