Question

Mr. E wants to have $200,000 in 5 years (when he retires) from an investment that earns

6.5% compounded semi-annually. How much will he need to invest now? (You are finding
the principal P)

Answer 1

Mr. E needs to invest approximately $147,233.35 now to have $200,000 in 5 years at an interest rate of 6.5% compounded semi-annually.

Step-by-step explanation:

To calculate the amount Mr. E needs to invest now, use the formula for compound interest: A = P(1 + r/n)^(nt), where A is the future value, P is the principal (initial investment), 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.

Given A = $200,000, r = 6.5% or 0.065, n = 2 (semi-annual compounding), and t = 5 years, the formula becomes 200,000 = P(1 + 0.065/2)^(2*5).

To solve for P, rearrange the formula and compute P = 200,000 / (1 + 0.065/2)^(2*5).

After calculations, Mr. E needs to invest approximately $147,233.35 now to accumulate $200,000 in 5 years with an interest rate of 6.5% compounded semi-annually. This calculation assumes the interest is compounded semi-annually, which accelerates the growth of the investment compared to annual compounding.