Ten years ago, Jane invested $1,000 and locked in a 7 percent annual interest rate for 30 years (end 20 years from now). James can made a 20-year investment today and lock in a 6 percent interest rate. How much money should he invest now in order to have the same amount of money in 20 years as Jane?

Question

Quizplus · Accepted Answer

Jane's investment grows according to the formula for compound interest: A = P(1 + r)^n, 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), and n is the time the money is invested for in years. For Jane, P = $1,000, r = 7% or 0.07, and n = 30 years. So, A = $1,000(1 + 0.07)^30 ≈ $7,612.26. James wants to have the same amount in 20 years, so using the formula with James's details where A = $7,612.26, r = 6% or 0.06, and n = 20 years, we solve for P: $7,612.26 = P(1 + 0.06)^20. Solving for P gives P ≈ $2,373.54.

Ten Years Ago, Jane Invested $1,000 and Locked in a 7