Question

Suppose you bought a 25-year annuity of $7,200 per year at the current discount rate of 9 percent per year

what is the value of your annuity today? (do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)

Answer 1

The present value of a 25-year annuity paying $7,200 annually at a discount rate of 9% can be determined using the present value of an annuity formula, which considers the time value of money.

Step-by-step explanation:

The student's question pertains to the calculation of the present value of an annuity. To determine the value of an annuity today, given a series of equal payments over time with a specified discount rate, a formula for the present value of an annuity should be used. This is an application of the time value of money concept, which states that a sum of money is worth more now than the same sum will be in the future due to its potential earning capacity. For a $7,200 per year 25-year annuity at a 9 percent discount rate, we need to apply the present value annuity formula:

Present Value of Annuity = Pmt * [(1 - (1 + r)^-n) / r]

Here, Pmt is the annuity payment ($7,200), r is the discount rate (0.09), and n is the total number of periods (25 years).

Using this formula, we can calculate the value of the annuity today.