Question

Terrance hopes to earn $600 in interest in 4.5years time from $⁢48,000 that he has available to invest. To decide if it's feasible to do this by investing in an account that compounds semi-annually, he needs to determine the annual interest rate such an account would have to offer for him to meet his goal. What would the annual rate of interest have to be? Round to two decimal places.

Answer 1

Terrance needs an annual interest rate of approximately 0.62%, compounded semi-annually, to earn $600 on a $48,000 investment over 4.5 years.

Step-by-step explanation:

To find the annual interest rate needed for Terrance to earn $600 in interest over 4.5 years on a $48,000 investment with semi-annual compounding, we use the future value formula for compound interest:

A = P(1 + r/n)^(nt), where A is the amount of money accumulated after n years, including interest, P is the principal amount, r is the annual interest rate, n is the number of times that interest is compounded per year, and t is the time the money is invested for in years.

We know that Terrance wants the future value (A) to be $48,600 (the original $48,000 plus $600 in interest), the principal (P) is $48,000, n is 2 (because interest is compounded semi-annually), and t is 4.5 years.

We need to solve for r in the equation $48,600 = $48,000(1 + r/2)^(2*4.5).

After rearranging the formula and solving for r, we find that the required annual interest rate is approximately 0.62% (rounded to two decimal places).