you deposit $4000 in an account earning 2% interest compounded continuously. how much will you have in the…

Explanation:

Step1: Recall continuous - compounding formula

The formula for continuous - compounding is $A = Pe^{rt}$, where $A$ is the amount of money in the account after $t$ years, $P$ is the principal amount (initial deposit), $r$ is the annual interest rate (in decimal form), and $t$ is the number of years.

Step2: Identify the values of $P$, $r$, and $t$

Given that $P=$4000$, $r = 0.02$ (since $2%=0.02$), and $t = 15$ years.

Step3: Substitute the values into the formula

$A=4000\times e^{0.02\times15}$. First, calculate the exponent: $0.02\times15 = 0.3$. Then, find the value of $e^{0.3}$. Using a calculator, $e^{0.3}\approx1.34985880757$. Now, multiply by the principal: $A = 4000\times1.34985880757$. $A\approx5399.44$.

Answer:

$5399.44$