Formula
An annuity is a financial instrument that provides a stream of fixed payments at regular intervals, typically monthly or annually. This annuity payment formula FV calculates the annuity payment required to provide a given value in the future FV (future value). The annuity formula assumes payments are made at the end of each period for n periods, and a discount rate i is applied.
Excel PMT Function
The Excel PMT function can be used instead of the annuity payment formula FV, and has the syntax shown below.
PMT(Rate, Nper, PV, FV, Type)
*In this instance, the PV and type arguments are not used when using the Excel annuity payment function.
Annuity Payment Formula FV Examples
The formula can be used to calculate the periodic deposits needed to provide a required savings account balance (FV).
Example 1
To illustrate suppose an investor wants to save an amount of 7,000 by depositing regular annuity payments. The payments are to be made for 14 periods at an interest rate of 3% per period. The amount of the annuity payment is given by the annuity payment formula FV as follows:
Annuity payment = Pmt = FV x i / ( (1 + i)n - 1 ) Annuity payment = Pmt = 7000 x 3% / ( (1 + 3%)14 - 1 ) Annuity payment = Pmt = 409.68
The same answer can be obtained using the Excel PMT function as follows:
Annuity payment = PMT(Rate, Nper, PV, FV, Type) Annuity payment = PMT(3%,14,,-7000) Annuity payment = 409.68
Example 2 Monthly Payments
To illustrate monthly payments suppose you require to have a future value of 90,000 after 15 years. Additionally the interest rate is given as 6% per year. In this case the calculation of the monthly annuity payment is as follows.
i = 6%/12 - 0.5% monthly n = 15 x 12 = 180 months Annuity payment = Pmt = FV x i / ( (1 + i)n - 1 ) Annuity payment = Pmt = 90000 x 0.5% / ( (1 + 0.5%)180 - 1 ) Annuity payment = Pmt = 309.47
In this case the monthly payment is 309.47. This payment results in a balance of 90,000 after 15 years at an annual interest rate of 6% compounded monthly.
In conclusion, the annuity payment formula FV is a useful tool for calculating the regular payment for different types of annuities. It is based on the future value formula and uses the interest rate, the number of payments, and the future value to determine the payment amount.
The payment formula FV is one of many used in time value of money calculations. Discover another at the links 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.