You invest some money and earn the following rates of interest: simple interest of 15% for 9 months,followed by j₆ = 12% for 18 months,followed by j₄ = 5% for 9 months.What is the equivalent rate of interest,j₂ earned over the 36 months?

Question

Quizplus · Accepted Answer

To find the equivalent rate of interest for 36 months, we need to calculate the total amount of interest earned and then find the rate that would yield the same amount of interest on the initial investment for 36 months.

Let's assume we invest $100.

1) Simple interest of 15% for 9 months = 15/12 * 9 = 11.25
Total amount = 100 + 11.25 = 111.25

2) Compound interest of 12% for 18 months = 100 * (1 + 12/100)^1.5 = 126.51
Total amount = 126.51

3) Compound interest of 5% for 9 months = 126.51 * (1 + 5/100)^0.75 = 133.02
Total amount = 133.02

Total interest earned = 133.02 - 100 = 33.02

To find the equivalent rate of interest for 36 months, we need to find the rate that would yield the same amount of interest on $100 for 36 months.

Using the formula, A = P(1 + r/n)^(nt), where A is the total amount, P is the principal, r is the annual interest rate, n is the number of times interest is compounded per year, and t is the time in years:

A = 100(1 + r/100)^(3*12)
33.02 = 100(1 + r/100)^(3*12)
1.3302 = (1 + r/100)^36
Taking the 36th root on both sides:
(1 + r/100) = 1.0103
r = 1.03 * 100 = 10.97%

Therefore, the equivalent rate of interest earned over 36 months is 10.97%, which is closest to option B (11.03%).

You Invest Some Money and Earn the Following Rates of Interest