you deposit $4000 in an account earning 7% interest compounded continuously. how much will you have in the…

you deposit $4000 in an account earning 7% interest compounded continuously. how much will you have in the account in 15 years?

Answer

The formula for continuous compound interest is $A = Pe^{rt}$, where:

$P$ = principal amount, $r$ = annual interest rate (decimal), $t$ = time in years, $A$ = final amount.

$P = 4000$, $r = 0.07$, $t = 15$

$A = 4000e^{(0.07 \times 15)}$

$0.07 \times 15 = 1.05$, so $A = 4000e^{1.05}$

$e^{1.05} \approx 2.85765$, so $A \approx 4000 \times 2.85765 = 11430.60$

$$11430.60$