On your tenth birthday, you received $100 which you invested at 4.5% interest, compounded annually. That investment is now worth $3,000. How old are you today?
A) age 77
B) age 82
C) age 84
D) age 86
E) age 87

Question

Quizplus · Accepted Answer

To find out how old you are today, you need to calculate how many years it took for the $100 to grow to $3,000 at an annual compound interest rate of 4.5%. The formula for compound interest is 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.Given that the interest is compounded annually, n = 1. The problem simplifies to finding t in the equation 3000 = 100(1 + 0.045)^t.Solving for t, we get:3000 = 100(1.045)^t30 = (1.045)^tTaking the natural logarithm (ln) of both sides gives:ln(30) = t * ln(1.045)t = ln(30) / ln(1.045)t ≈ 77Since this investment started on your 10th birthday, you add those 77 years to your initial age of 10:10 + 77 = 87Therefore, you are 87 years old today.

On Your Tenth Birthday, You Received $100 Which You Invested