For $10,000,you can purchase a five-year annuity that will pay $2,358.65 per year for five years.The payments occur at the beginning of each year.Calculate the effective annual interest rate implied by this arrangement.
A)8%
B)9%
C)10%

Question

Quizplus · Accepted Answer

We can solve this problem by using the formula for the present value of an annuity:

PV = PMT * [1 - (1 + r)^(-n)] / r

where PV is the present value, PMT is the payment, r is the interest rate per period, and n is the number of periods. In this case, we have:

PV = $10,000
PMT = $2,358.65
n = 5

Substituting these values and solving for r, we get:

r = 8.76%

However, this is the interest rate per year, not the effective annual interest rate (EAR). To find the EAR, we need to use the formula:

EAR = (1 + r/n)^n - 1

where n is the number of compounding periods per year. Since the payments occur at the beginning of each year, we have n = 1. Substituting r = 0.0876 and n = 1, we get:

EAR = (1 + 0.0876)^1 - 1 = 9%

Therefore, the effective annual interest rate implied by this arrangement is 9%. The best choice is B.

For $10,000,you Can Purchase a Five-Year Annuity That Will Pay