you deposit $5000 in an account earning 5% interest compounded continuously. how much will you have in the…

Explanation:

Step1: Identify the 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: Convert the interest rate to decimal

Given $r = 5%=0.05$, $P = 5000$, and $t = 15$.

Step3: Substitute values into the formula

$A=5000\times e^{0.05\times15}$.

Step4: Calculate the exponent

First, calculate $0.05\times15 = 0.75$. Then, find $e^{0.75}$. Using a calculator, $e^{0.75}\approx2.117$.

Step5: Calculate the final amount

$A = 5000\times2.117=10585$.

Answer:

$10585$