Using the Future Value of Annuity Due Formula
The future value of an annuity due 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 start of each period for n periods, and a discount rate i is applied.
In this case the formula compounds the value of each payment forward to its value at the end of period n (future value).
Excel Function
Additionally the Excel FV function can replace the future value of an annuity due formula. The function has the syntax shown below.
FV = FV(i, n, pmt, PV, type)
*The Excel future value of an annuity due function does not use the PV argument.
Future Value of an Annuity Due Formula Examples
Example 1
To illustrate suppose an investor receives 3,000 at the start of each period for 7 periods. Additionally the discount rate is 8%. Using the FV annuity due formula the value of the receipts at the end of period 7 is 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 Excel FV function gives the same answer as follows:
FV = FV(i, n, Pmt,,1) FV = FV(8%,7,-3000,,1) FV = 28,909.88
* It is important to realize that this is an annuity due calculation. Consequently the receipts are at the start of each period and therefore the Type argument in the Excel FV function is 1.
Example 2
In a similar fashion, suppose a saver decides to deposit the amount of 4,000 into a bank account at the start of each year. The saver intends to continue with the regular deposits for 12 years. The interest rate on the bank account is 5%.
The calculation of the future value of the saving deposits is as follows.
FV = Pmt x (1 + i) x ( (1 + i)n - 1 ) / i FV = 4,000 x (1 + 5%) x ( (1 + 5%)12 - 1 ) / 5% FV = 66,851.93
At the end of the 12 year period the deposits will be worth 66,851.93
Again the Excel FV function gives the same answer as follows:
FV = FV(i, n, Pmt,,1) FV = FV(5%,12,-4000,,1) FV = 66,851.93
The FV annuity due 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.