The formula for calculating the present value of an ordinary annuity is:
P = PMT [(1 - (1 / (1 + r)n)) / r]
P = The present value of the annuity stream to be paid in the future
PMT = The amount of each annuity payment
r = The interest rate
n = The number of periods over which payments are made
For example, ABC International has commited to make a legal settlement in the amount of $50,000 per year for each of the next ten years. What would it cost ABC if it were to settle the claim immediately, assuming an interest rate of 5%? The calculation is:
P = $50,000 [(1 - (1/(1+.05)10))/.05]
P = $386,087
As another example, ABC International is contemplating the acquisition of a machinery asset. The supplier offers a financing deal under which ABC can pay $500 per month for 36 months, or the company can pay $15,000 in cash right now. The current market interest rate is 9%. Which is the better offer? The calculation of the present value of the annuity is:
P = $500 [(1 - (1/(1+.0075)36))/.0075]
P = $15,723.40
Since the up-front cash payment is less than the present value of the 36 monthly lease payments, ABC should pay cash for the machinery.
In the calculation, we convert the annual 9% rate to a monthly rate of 3/4%, which is calculated as the 9% annual rate divided by 12 months.
Future value of an ordinary annuity table
Present value of an ordinary annuity table
What is an ordinary annuity?
What is the formula for the future value of an ordinary annuity?
What is the formula for the present value of an annuity due?