The following formula is used to calculate the present value of an ordinary annuity:
\[ PV = PMT \times \left( \frac{1 - (1 + r)^{-n}}{r} \right) \]
Where:
To calculate the present value of an ordinary annuity, multiply the periodic payment by the factor \(\left( \frac{1 - (1 + r)^{-n}}{r} \right)\), where \(r\) is the interest rate per period, and \(n\) is the number of periods.
An ordinary annuity is a series of equal payments made at the end of consecutive periods over a fixed length of time. It’s a common financial product used in retirement plans and loans. The present value of an ordinary annuity is the total value of all future payments discounted to their value today, considering a specific interest rate.
Let's say you have an ordinary annuity with periodic payments of $500, an interest rate per period of 5% (0.05 as a decimal), and the number of periods is 10. Using the formula:
\[ PV = 500 \times \left( \frac{1 - (1 + 0.05)^{-10}}{0.05} \right) \]
Calculating this step-by-step:
\[ PV = 500 \times \left( \frac{1 - (1.05)^{-10}}{0.05} \right) \]
\[ PV = 500 \times \left( \frac{1 - 0.61391}{0.05} \right) \]
\[ PV = 500 \times \left( \frac{0.38609}{0.05} \right) \]
\[ PV = 500 \times 7.7218 = 3860.90 \]
So, the present value of the ordinary annuity is $3,860.90.