Future Value of Ordinary Annuity
The future value of an ordinary annuity refers to the accumulated amount of money at some future date from a series of equal payments (or receipts) made at regular intervals (end of each period). An “ordinary annuity” assumes that these cash flows occur at the end of each period.
The future value of an ordinary annuity can be calculated using the following formula:
\(FV = P \times \frac{(1 + r)^n – 1}{r} \)
Where:
- FV = Future Value
- P = Payment amount per period
- r = interest rate per period
- n = total number of payments (or periods)
Example of Future Value of Ordinary Annuity
Suppose you plan to deposit $200 at the end of each year into a savings account that pays an annual interest rate of 3%. You plan to do this for 10 years.
For this example, the values are:
- P = $200
- r = 0.03
- n = 10
Substitute these values into the formula:
\(FV = \$200 \times \frac{(1 + 0.03)^10 – 1}{0.03} \)
\(= \$200 \times \frac{1.34392 – 1}{0.03} \)
\(= \$200 \times \frac{ 0.34392}{0.03} \)
= $2,293.08
So, the future value of the ordinary annuity (the amount you’ll have in your savings account after 10 years) would be approximately $2,293.08.
This example demonstrates how regular saving and compound interest can help grow your money over time.
