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.
About the Author
Chartered accountant Michael Brown is the founder and CEO of Double Entry Bookkeeping. He has worked as an accountant and consultant for more than 25 years and has built financial models for all types of industries. He has been the CFO or controller of both small and medium sized companies and has run small businesses of his own. He has been a manager and an auditor with Deloitte, a big 4 accountancy firm, and holds a degree from Loughborough University.