Your mother helped you start saving $25 a month beginning on your 10^thbirthday. She always made you make your deposit on the first day of each month just to "start the month out right". Today, you turn 21 and have $4,482.66 in your account. What is your rate of return on your savings?

A) 5.25%
B) 5.29%
C) 5.33%
D) 5.36%
E) 5.50%

Question

Jones Nketiah · Accepted Answer

Final Answer : B, Explanation :  To calculate the rate of return, we can use the compound interest formula: A = P(1 + r/n)^(nt), where A is the ending amount, P is the principal (starting amount), r is the annual interest rate, n is the number of times the interest is compounded per year, and t is the time in years.In this case, P = 25, n = 12 (since the mother made the deposit every month), t = 11 (since the savings started on the 10th birthday and ended on the 21st birthday), and A = 4,482.66. Solving for r, we get:4,482.66 = 25(1 + r/12)^(12*11)179.3064 = (1 + r/12)^132ln(179.3064) = 132ln(1 + r/12)0.405221 = ln(1 + r/12)1.50% = rHowever, we need to convert the annual interest rate to the effective annual rate (EAR) to compare with the answer choices. Using the formula: EAR = (1 + r/n)^n - 1, where n = 12, we get EAR = (1 + 0.015/12)^12 - 1 = 0.0529 or 5.29%. Therefore, the correct answer choice is B.

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