Compound Interest Factors

The Compound Interest Factors calculation lets you calculate any of the eight common compound interest factors for a given rate and number of periods and lets you easily set up a compound interest factor table.

FinKit uses these factors internally in many of the calculations.

Factor notation

The convention used to denote factors is in the form (F/P, i %, n). This factor indicates that we are trying to compute the future value F, of a present value P, with an interest rate of i % per period for n periods. In the example below, P is $20,000, i is 12 %, and n is 15 periods.  When the present value is multiplied by this factor the result is the future value at the end of 15 periods.

Discrete compounding

When interest periods coincide with payment periods, it's possible to make direct use of the interest factors: just enter the effective periodic rate and the total number of interest periods.

When interest periods are smaller than payment periods, interest may be compounded multiple times per payment periods. A convenient method is to convert the nominal interest rate to an equivalent effective interest rate for the given payment period.

When interest periods are larger than payment periods, some payments may not have been deposited for an entire interest period. It may be that such payments do not earn interest at all, or that they only generate a fraction in proportion to the elapsed time. In these situations FinKit also calculates using an equivalent effective interest rate.

Continuous compounding

When the interest periods become infinitesimally small, then compounding is said to be continuous. In the case of continuous compounding, the nominal annual rate is stated instead of the effective periodic rate.

Note: FinKit displays factors based on discrete compounding between normal brackets "(" and ")", and uses square brackets "[" and "]" to indicate continuous compounding.

Input

• effective periodic rate or nominal annual rate
• compounding type
• interest factor set
• number of periods

Results

Depending on which set of factors is selected:
• (P/F, i %, n) : single payment present value factor
• (F/P, i %, n) : single payment future value factor
• (A/P, i %, n) : uniform series capital recovery factor
• (P/A, i %, n) : uniform series present value factor

• (A/F, i %, n) : uniform series sinking fund factor

• (F/A, i %, n) : uniform series future value factor
• (A/G, i %, n) : arithmetic gradient to uniform series factor
• (P/G, i %, n) : arithmetic gradient present value factor

Example

What is the future value of an amount of $20,000 at 12 % compounded annually after 15 years?

First we calculate the appropriate factor:

Input Effective periodic rate: 12 %
  Compounding type discrete
  Interest factors: single payment
  Number of periods: 15
     
Result (F/P, 12 %, 15) 5.473566

Then we multiply the present value by the factor:

Answer: $20,000 x 5.473566 = 109,471.32.

Note: the same result can be obtained using the Single Payment calculation and entering the $20,000 amount directly.

 

Related topic

Compound interest