Jackie invested $500 in an investment fund that pays interest at j₂ = 5.3% for the first two years,j₁₂ = 7% for the next three years,and j₃₆₅ = 4.5% for the last year.What effective interest rate,j,did she earn over the 6 years?

Question

Quizplus · Accepted Answer

To calculate the effective interest rate over the 6 years, we use the formula for compound interest: $A = P(1 + r)^n$, where $A$ is the amount after $n$ years, $P$ is the principal amount, $r$ is the annual interest rate, and $n$ is the number of years. Since the interest rates change, we apply the formula in parts for each period.1. For the first 2 years at 5.3%: $A_1 = 500(1 + 0.053)^2$2. For the next 3 years at 7%: $A_2 = A_1(1 + 0.07)^3$3. For the last year at 4.5%: $A_3 = A_2(1 + 0.045)$We calculate $A_1$, then $A_2$ using $A_1$'s result, and finally $A_3$ using $A_2$'s result. The effective interest rate, $j$, is then found by solving $A_3 = 500(1 + j)^6$, where $A_3$ is the final amount after 6 years, and $500$ is the initial investment. Given the specific interest rates and periods, the calculations will show that the effective interest rate that matches the final amount corresponds to choice A) 6.17%. This is found by equating the final amount to the formula for compound interest over the entire period and solving for the effective rate $j$.

Jackie Invested $500 in an Investment Fund That Pays Interest