If it were evaluated with an interest rate of 0 percent,a 10-year regular annuity would have a present value of $3,755.50.If the future (compounded)value of this annuity,evaluated at Year 10,is $5,440.22,what effective annual interest rate must the analyst be using to find the future value?
A) 7%
B) 8%
C) 9%
D) 10%
E) 11%

Question

Quizplus · Accepted Answer

The future value of an annuity can be calculated using the formula FV = P * [(1 + r)^n - 1] / r, where P is the payment, r is the interest rate per period, and n is the number of periods. Given the present value, we can find the annual payment (P) first by dividing the present value by the number of periods (since the interest rate is 0%, the present value is simply the total of the payments). $3,755.50 / 10 = $375.55. Using the future value of $5,440.22, we can set up the equation $5,440.22 = $375.55 * [(1 + r)^10 - 1] / r and solve for r. Solving this equation gives an interest rate close to 8%, making option B the correct answer.

If It Were Evaluated with an Interest Rate of 0