Question

Assuming a 12% annual interest rate, determine the present value of a five-period annual annuity of $5,900 ---The first payment is received at the end of the first year, and interest is compounded quarterly.

Answer 1

The present value of a five-period annual annuity with a 12% interest rate compounded quarterly is calculated by summing the present value of each $5,900 payment discounted at the adjusted quarterly rate over each of the 5 years.

Step-by-step explanation:

To determine the present value of a five-period annual annuity of $5,900 with a 12% annual interest rate, you must calculate the present value of each annuity payment and then sum these values. The interest rate must be adjusted to account for quarterly compounding before applying the present value formula.

For each payment, the present value is calculated as follows:

Present Value = Annuity Payment / (1 + r/n)nt

Where Annuity Payment is $5,900, r is the annual interest rate (0.12), n is the number of compounds per year (4 for quarterly), and t is the time in years. We calculate the present value for each of the 5 years separately and sum these amounts to get the total present value of the annuity.