Koji invested $3,300 at 7.75% interest. After a period of time he withdrew $9,383.31. How long did Koji have his money invested?

Question

Quizplus · Accepted Answer

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. In this case, since the interest rate is given as an annual rate and there's no indication that it's compounded more frequently than once a year, we can simplify the formula to A = P(1 + r)^t. We're given that A = $9,383.31, P = $3,300, and r = 7.75% or 0.0775 in decimal form. We need to solve for t. Rearranging the formula to solve for t gives us t = log(A/P) / log(1 + r). Plugging in the numbers gives us t = log(9383.31/3300) / log(1 + 0.0775), which calculates to approximately 14 years.

Koji Invested $3,300 at 7