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?

A) $19,000.19
B) $11,535.60
C) $10,691.38
D) $8,800.00

To find the amount in the account when Jackson is 40, we use the formula for continuous compounding interest, $A=P{e}^{rt}$ , 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.