Question

example: brenda invests $30,000 in a retirement fund with a fixed annual interest rate of 6.5% compounded continuously. what will the account balance be after 8 years?

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), and $t$ is the time in years.

Step2: Substitute the values

Given $P=\$30000$, $r = 0.065$ (since $6.5\%=0.065$), and $t = 8$. Substitute into the formula: $A=30000\times e^{0.065\times8}$.

Step3: Calculate the exponent

First, calculate $0.065\times8 = 0.52$. So the formula becomes $A = 30000\times e^{0.52}$.

Step4: Evaluate $e^{0.52}$

Using a calculator, $e^{0.52}\approx1.6823$.

Step5: Calculate $A$

Multiply $30000\times1.6823=\$50469$.

Answer:

The account balance after 8 years will be approximately $\$50469$.