Factor Formulas

The table below summarizes the equivalency factors . The Name column shows the traditional names for the factors. Each factor has a formula that depends on i, the interest rate per compounding period, and N, the number of compounding periods in the interval. The factors are valid for i strictly greater than zero and N integer.

Factor

Name

Formula

Purpose

(F/P, i, N)

Single payment compound amount factor

Moves a single payment to N periods later in time

(P/F, i, N)

Single payment present worth factor

Moves a single payment to N periods earlier in time

(A/F, i, N)

Sinking Fund factor

Takes a single payment and spreads into a uniform series over N earlier periods. The last payment in the series occurs at the same time as F.

(F/A, i, N)

Uniform Series Compound Amount factor

Takes a uniform series and moves it to a single value at the time of the last payment in the series.

(A/P, i, N)

Capital Recovery Factor

Takes a single payment and spreads it into a uniform series over N later periods. The first payment in the series occurs one period later than P.

(P/A, i, N)

Uniform Series Present Worth Factor

Takes a uniform series and moves it to a single payment one period earlier than the first payment of the series.

(P/G, i, N)

Arithmetic Gradient Present Worth Factor

Takes a arithmetic gradient series and moves it to a single payment two periods earlier than the first nonzero payment of the series.

(A/G, i, N)

Arithmetic Gradient to Uniform Series Factor

Takes a arithmetic gradient series and converts it to a uniform series. The two series cover the same interval, but the first payment of the gradient series is 0.