The Time Value of Money

Single Amount

Measure the value of an amount that is allowed to grow at a given interest rate over a period of time

FV = PV(1 + i)^n

Annuity

Series of consecutive payments or receipts of equal amount

FVA = P * ([1 + I]^N - 1 )/I

Single Amount

Formula derived from the original formula for future value

FV[I/(1+i)^n]

Annuity

Each individual payment is discounted back to the present and then all of the discounted payments are added up

P[(1-(1+i)^-1/i)]

Present Value of a Single Amount

The determination of PVIF does not give us the final answer, but it scales down the problem so we may ascertain the answer

PVIF=PV/FV

Present Value of an Annuity

Same type of approximated or interpolated yield that applied to a single amount can also be applied

PVIFA=PVA/A

Patterns of Payment

Time value of money problems may evolve around a number of different payment or receipt patterns

To determine n

Multiply the number of years by the number of compounding periods during the year

The factor for i

Is then determined by dividing the quoted annual interest rate by the number of compounding periods