(Ignore income taxes in this problem.) You have deposited $16,727 in a special account that has a guaranteed interest rate. If you withdraw $4,300 at the end of each year for 5 years, you will completely exhaust the balance in the account. The guaranteed interest rate is closest to:
A) 6%
B) 29%
C) 9%
D) 26%

Question

Quizplus · Accepted Answer

After withdrawing $4,300 each year for 5 years, the total amount withdrawn will be $21,500. Therefore, the interest earned over the 5-year period is $21,500 - $16,727 = $4,773. 
Using the formula for compound interest: 
A = P(1 + r/n)^(nt), where A = final amount, P = principal, r = annual interest rate, n = number of times interest is compounded per year, t = time in years 
Plugging in the values we know: 
$21,500 = $16,727(1 + r/n)^(5)
Simplifying: 
1.282 = (1 + r/n)^(5)
Taking the fifth root of both sides: 
1.032 =~ 1 + r/n 
0.032 =~ r/n 
The interest rate would be n*r = 12*0.032 = 0.384 or approximately 0.38. Therefore, the closest interest rate from the choices given is 9%.

(Ignore Income Taxes in This Problem