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

Explanation:

Step1: Identify principal value

The principal $P$ is the initial deposit. Here, $P = 1000$.

Step2: Identify interest - rate and time

The annual interest rate $r=8.5%=0.085$ and the time $t = 5$ years.

Step3: Use continuous - compounding formula

The formula for continuous compounding is $A=Pe^{rt}$, where $A$ is the final amount, $P$ is the principal, $r$ is the annual interest rate, and $t$ is the time in years. Substitute $P = 1000$, $r=0.085$, and $t = 5$ into the formula: $A = 1000\times e^{0.085\times5}$.

Step4: Calculate the exponent

First, calculate $0.085\times5=0.425$. Then, find the value of $e^{0.425}$. Using a calculator, $e^{0.425}\approx1.5299$.

Step5: Calculate the final amount

Multiply $1000$ by $e^{0.425}$: $A=1000\times1.5299 = 1529.92$.

Answer:

$1529.92$