On your thirteenth birthday, you received $1,000 which you invested at 6.5% interest, compounded annually. Your investment is now worth $5,476. How old are you today?
A) age 29
B) age 32
C) age 35
D) age 37
E) age 40

Question

Quizplus · Accepted Answer

To find out how old you are today, you need to calculate how many years it took for the initial investment of $1,000 to grow to $5,476 at an annual compound interest rate of 6.5%. The formula for compound interest is 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 number of years the money is invested for.Rearranging the formula to solve for n gives us n = log(A/P) / log(1 + r).Plugging in the values from the problem gives us n = log(5476/1000) / log(1 + 0.065) = log(5.476) / log(1.065) ≈ 27.Since the investment started on your 13th birthday, you add these 27 years to 13 to find out your current age, which is 40.

On Your Thirteenth Birthday, You Received $1,000 Which You Invested