Future Value of Annuities
An annuity is a series of equal payments or receipts that occur at evenly spaced intervals. Leases and rental payments are examples. The payments or receipts occur at the end of each period for an ordinary annuity while they occur at the beginning of each period.for an annuity due.
Future Value of an Ordinary Annuity
The Future Value of an Ordinary Annuity (FVoa) is the value that a stream of expected or promised future payments will grow to after a given number of periods at a specific compounded interest.
The Future Value of an Ordinary Annuity could be solved by calculating the future value of each individual payment in the series using the future value formula and then summing the results. A more direct formula is:
Example: What amount will accumulate if we deposit $5,000 at the end of each year for the next 5 years? Assume an interest of 6% compounded annually.
PV = 5,000
FVoa = 5,000 [ (1.3382255776 - 1) /.06 ] = 5,000 (5.637092) = 28,185.46
Example 2: In practical problems, you may need to calculate both the future value of an annuity (a stream of future periodic payments) and the future value of a single amount that you have today:
For example, you are 40 years old and have accumulated $50,000 in your savings account. You can add $100 at the end of each month to your account which pays an interest rate of 6% per year. Will you have enough money to retire in 20 years?
You can treat this as the sum of two separate calculations:
PMT = $100 per period
FVoa = 100 [ (3.3102 - 1) /.005 ] = 46,204
PV = 50,000 Present value (the amount you have today)
FV = PV (1+i)240 = 50,000 (1.005)240 = 165,510.22
After 20 years you will have accumulated $211,714.22 (46,204.00 + 165,510.22).
Future Value of an Annuity Due (FVad)
The Future Value of an Annuity Due is identical to an ordinary annuity except that each payment occurs at the beginning of a period rather than at the end. Since each payment occurs one period earlier, we can calculate the present value of an ordinary annuity and then multiply the result by (1 + i).
Example: What amount will accumulate if we deposit $5,000 at the beginning of each year for the next 5 years? Assume an interest of 6% compounded annually.
PV = 5,000
FVoa = 28,185.46 (1.06) = 29,876.59
Combined FormulaYou can also combine these formulas and the future value of a single amount formula into one.
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