When you were 26 years old, you received an inheritance of $1,500 from your grandfather. You invested that amount in Nu-Wave stock and have not touched the investment since then. Today, this investment is worth $109,533.59. Nu-Wave stock has earned an average rate of return of 11.3% per year over this time period. How old are you today?
A) age 57
B) age 59
C) age 62
D) age 64
E) age 66

Question

Quizplus · Accepted Answer

To find out how old you are today, you can use the formula for compound interest: $A = P(1 + r)^t$, 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 $t$ is the time the money is invested for in years. Rearranging the formula to solve for $t$, we get $t = \frac{\log(A/P)}{\log(1 + r)}$.Given:- $A = \$109,533.59$- $P = \$1,500$- $r = 11.3\% = 0.113$Plugging in the values:$t = \frac{\log(109533.59/1500)}{\log(1 + 0.113)}$$t = \frac{\log(73.02239333)}{\log(1.113)}$$t \approx 40$ yearsSince you were 26 years old when you received the inheritance and invested it, and 40 years have passed since then, you are now:$26 + 40 = 66$ years old.

When You Were 26 Years Old, You Received an Inheritance