FV = Pmt x ( (1 + i)n - 1 ) / i
FV = Future Value
Pmt = Periodic payment
i = Discount rate
n = Number of periods
The future value annuity formula shows the value at the end of period n of a series of regular payments. The payments are made at the end of each period for n periods, and a discount rate i is applied.
The formula compounds the value of each payment forward to its value at the end of period n (future value).
The Excel FV function can be used instead of the future value annuity formula, and has the syntax shown below.
FV = FV(i, n, pmt, PV, type)
*The PV and type arguments are not used when using the Excel future value of an annuity function.
Future Value Annuity Formula Example
If a payment of 5,000 is received at the end of each period for 10 periods, and the discount rate is 4%, then the value of the payments at the end of period 10 is given by the future value annuity formula as follows:
FV = Pmt x ( (1 + i)n - 1 ) / i FV = 5,000 x ( (1 + 4%)10 - 1 ) / 4% FV = 60,030.54
The same answer can be obtained using the Excel PV function as follows:
FV = FV(i, n, Pmt) FV = FV(4%,10,-5000) FV = 60,030.54
The future value of annuity formula is one of many annuity formulas used in time value of money calculations, discover another at the link below.