Today, your grandmother gave you a gift of $25,000 to help pay for your college education. She told you that this amount was the result of a one-time investment at 8% interest 13 years ago. How much did your grandmother originally invest?

Question

Quizplus · Accepted Answer

To find the original investment, 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. Since the interest is compounded annually (implied by the lack of information to the contrary), n = 1. Given A = $25,000, r = 8% or 0.08, and t = 13 years, we solve for P: $25,000 = P(1 + 0.08/1)^(1*13), which simplifies to $25,000 = P(1.08)^13. Solving for P gives approximately $9,192.45.

Today, Your Grandmother Gave You a Gift of $25,000 to Help