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.

FactorNameFormulaPurpose
(F/P, i, N)Single payment compound amount factorMoves a single payment to N periods later in time
(P/F, i, N)Single payment present worth factorMoves a single payment to N periods earlier in time
(A/F, i, N)Sinking Fund factorTakes 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 factorTakes 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 FactorTakes 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 FactorTakes 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 FactorTakes 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 FactorTakes 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.

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