$1500 are deposited in an account with 6% interest rate, compounded continuously. what is the balance after…

Explanation:

Step1: Identify the formula

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

Step2: Convert the interest rate to decimal

Given $r = 6%=0.06$, $P=$1500$, and $t = 5$ years.

Step3: Substitute values into the formula

$A=1500\times e^{0.06\times5}$. First, calculate the exponent: $0.06\times5 = 0.3$. Then, find $e^{0.3}$. Using a calculator, $e^{0.3}\approx1.3498588076$. Multiply by the principal: $A = 1500\times1.3498588076$. $A\approx2024.79$.

Answer:

$2024.79$