FV = Pmt x (1 + i) x ( (1 + i)n - 1 ) / i
FV = Future Value
Pmt = Periodic payment
i = Discount rate
n = Number of periods
The future value of an annuity due formula shows the value at the end of period n of a series of regular payments. The payments are made at the start 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 of an annuity due formula, and has the syntax shown below.
FV = FV(i, n, pmt, PV, type)
*The PV argument is not used when using the Excel future value of an annuity due function.
Example Using the Future Value of an Annuity Due Formula
If a payment of 3,000 is received at the start of each period for 7 periods, and the discount rate is 8%, then the value of the payments at the end of period 7 is given by the future value annuity due formula as follows:
FV = Pmt x (1 + i) x ( (1 + i)n - 1 ) / i FV = 3,000 x (1 + 8%) x ( (1 + 8%)7 - 1 ) / 8% FV = 28,909.88
The same answer can be obtained using the Excel FV function as follows:
FV = FV(i, n, Pmt,,1) FV = FV(8%,7,-3000,,1) FV = 28,909.88
The future value of an annuity due formula is one of many annuity formulas used in time value of money calculations, discover another at the link below.