$8500 are deposited in an account with 7% interest rate, compounded continuously. what is the balance after…

Explanation:

Step1: Recall continuous - compounding 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 $r = 7%=0.07$, $P = 8500$, and $t = 16$.

Step3: Substitute the values into the formula

$A=8500\times e^{0.07\times16}$. First, calculate the exponent: $0.07\times16 = 1.12$. Then, find the value of $e^{1.12}$. Using a calculator, $e^{1.12}\approx3.06387$. Multiply by the principal: $A = 8500\times3.06387$. $A=8500\times3.06387 = 26042.895\approx26042.90$.

Answer:

$26042.90$