Your grandmother invested a lump sum 26 years ago at 4.25 percent interest.Today,she gave you the proceeds of that investment which totaled $51,480.79.How much did she originally invest?

Question

Quizplus · Accepted Answer

To find the original investment amount, we use the 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 (the initial amount of money), r is the annual interest rate (decimal), n is the number of times that interest is compounded per year, and t is the time the money is invested for in years. In this case, we are given A = $51,480.79, r = 4.25% or 0.0425, n = 1 (assuming the interest is compounded annually for simplicity), and t = 26 years. We need to solve for P.Rearranging the formula to solve for P gives us P = A / (1 + r/n)^(nt).Plugging in the given values: P = $51,480.79 / (1 + 0.0425)^(26) = $51,480.79 / (1.0425)^(26).Calculating this gives us P ≈ $17,444.86, which matches option C.

Your Grandmother Invested a Lump Sum 26 Years Ago at 4.25