$1000 are deposited in an account with a 8.5% interest rate, compounded continuously. what is the balance…

Explanation:

Step1: Identify the formula

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

Step2: Convert the interest rate to decimal

The interest rate $r = 8.5%=0.085$, and the principal amount $P = 1000$, and the time $t = 5$.

Step3: Substitute the values into the formula

$A=1000\times e^{0.085\times5}$. First, calculate the exponent: $0.085\times5 = 0.425$. Then, find the value of $e^{0.425}$. Using a calculator, $e^{0.425}\approx1.52994$. Multiply by the principal: $A = 1000\times1.52994 = 1529.94$.

Answer:

$1529.94$