Legacy Document

compound

You can use the compound function to determine the compound interest earned given an interest rate and period.

double_t compound (double_t rate, double_t periods);

rate

The interest rate (any positive floating-point number).

periods

The number of interest periods (any positive floating-point number). This argument might or might not be an integer.

DESCRIPTION

The compound function computes the compound interest earned.

$compound(r,n)\; =\; (1+r)n$

When rate is a small number, use the function call compound(rate,n) instead of the function call pow((1 + rate),n). The call compound(rate,n) produces a more exact result because it avoids the roundoff error that might occur when the expression
1 + rate is computed.

The compound function is directly applicable to computation of present and future values:

$PV\; =\; FV\times (1+r)-n=\; FV\; OVER\; compound(r,n)$

$FV\; =\; PV\times (1+r)n=\; PV\times compound(r,n)$

where PV is the amount of money borrowed and FV is the total amount that will be paid on the loan.

EXCEPTIONS

When r and n are finite and nonzero, the result of $compound(r,n)$ might raise one of the following exceptions:

• inexact (for all finite, nonzero values of r > -1)
• invalid (if r < -1)
• divide-by-zero (if r is -1 and n < 0)

SPECIAL CASES

Table 10-33 shows the results when one of the arguments to the compound function is a zero, a NaN, or an Infinity, plus other special cases for the compound function. In this table, r and n are finite, nonzero floating-point numbers.

Special cases for the compound function

Operation	Result	Exceptions raised
$compound(r,n)$ for r < -1	NaN	Invalid
$compound(-1,n)$	0 if n > 0	None
	+ if n < 0	Divide-by-zero
$compound(+0,n)$	1	None
$compound(r,+0)$	1	None
$compound(-0,n)$	1	None
$compound(r,-0)$	1	None
$compound(\pm 0,\pm$ )	NaN	Invalid
$compound(NaN,n)$	NaN[55]	None[56]
$compound(r,NaN)$	NaN	None
$compound(+$ ,n)	+ if n > 0	None
	0 if n < 0	None
$compound(r,+$ )	+	None
$compound(-$ ,n)	NaN	Invalid
$compound(r,-$ )	0	None

EXAMPLES

z = compound(-2, 12);   /* z = NAN because a negative interest 
                           rate does not make sense. The invalid 
                           exception is raised. */
z = compound(-1, -1);   /* z = +INFINITY because a negative 
                           interest rate and negative loan period 
                           do not make sense. The divide-by-zero 
                           exception is raised. */
z = compound(0, INFINITY);/* z = NAN. The invalid exception is 
                           raised. */

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[55] If both arguments are NaNs, the first NaN is returned.

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[56] If the NaN is a signaling NaN, the invalid exception is raised.