Jackson deposited $5,000 at 3.8% interest,compounded continuously,when he was 18 years old.How much will be in the account when he is 40 years old if he made no other deposits or withdrawals?

Question

Quizplus · Accepted Answer

To find the amount in the account when Jackson is 40, we use the formula for continuous compounding interest, $A = Pe^{rt}$, 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 deposited for in years. Here, $P = $5,000$, $r = 3.8\% = 0.038$, and $t = 40 - 18 = 22$ years. Plugging these values into the formula gives us $A = 5000e^{0.038 \times 22}$, which calculates to approximately $11,535.60.

Jackson Deposited $5,000 at 3