Formula and Use
The future value annuity formula shows the value at the end of period n of a series of regular payments. It is important to realize that 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). In the formula the terms have the following meaning.
Periodic Payment (Pmt) This refers to the amount of money paid on a regular basis, such as monthly or yearly. It is important that the payments are equal in size and occur at equal intervals at the end of a period.
Interest Rate (i) This is the rate at which the money invested in the annuity grows over time. It is usually expressed as a percentage.
Number of Periodic Payments (n) This is the number of times the periodic payments are made. For example, if the payments are made monthly for five years, then n would be 60 (12 months x 5 years).
Excel Function
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
To illustrate suppose a payment of 5,000 is received at the end of each period for 10 periods. Additionally a discount rate of 4% is applied. 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 FV of annuity formula is one of many annuity formulas used in time value of money calculations. Discover another at the link below.