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Discrete Compounding Formulas

Discrete compounding formulas with discrete payments

Single Payment

Compound Amount - Symbol (F/P, i%, n)

Converts to a future value - F - given a present single payment or value - P - today.

F = P [(1 + i)ⁿ] (1)

where

F = future value

P = single payment today

i = interest rate per period

n = number of periods

single payment present amount diagram

Compound Amount - Online Calculator

P - single payment today

i - interest rate (%)

n - number of periods

Present Worth - Symbol (P/F, i%, n)

Converts to a present value - P - given a future payment or value - F.

P = F [(1 + i)^-n] (2)

where

P = present value

F = single future payment

i = discount rate per period

n = number of periods

single payment compound amount diagram

Present Value - Online Calculator

F - single future payment

i - discount rate (%)

n - number of periods

Uniform Series

Compound Amount - Symbol (F/A, i%, n)

Converts to a future value - F - given a uniform amount, annuity - A - per interest period

F = A [( (1 + i)ⁿ -1 ) / i ] (3)

where

F = future value

A = uniform amount per period

i = interest rate

n = numbers of periods

uniform series compound amount diagram

Compound Amount - Online Calculator

A - uniform amount per period

i - interest rate (%)

n - number of periods

Sinking Fund - Symbol (A/F, i%, n)

Converts to a uniform amount, annuity - A - per interest period a given specific future value - F

A = F [i/((1 + i)ⁿ - 1)] (4)

where

A = uniform amount per period

F = future value

i = interest rate

n = number of periods

uniform series sinking fund diagram

Sinking Fund - Online Calculator

F - future value

i - interest rate (%)

n - number of periods

Present Worth - Symbol (P/A, i%, n)

Converts a uniform amount, annuity - A - per interest period to a present value - P

P = A [((1 + i)ⁿ - 1) / ( i (1+i)ⁿ)] (5)

where

P = present value

A = amount per interest period

i = discount rate

n = discount periods

uniform series present wort value diagram

Present Worth or Value - Online Calculator

A - uniform amount per interest period

i - discount rate (%)

n - number of periods

Capital Recovery - Symbol (A/P, i%, n)

Converts a present value - P - to a uniform amount, annuity - A - per interest period

A = P [(i (1 + i)ⁿ) / ((1+i)ⁿ - 1)] (6)

where

P = present value

A = amount per interest period

i = interest rate

n = discount periods

uniform series capital recovery diagram