if your interest rate is 4.5% compounding continuously, how much money do you have if you invest $1000 for…

Explanation:

Step1: Recall continuous - compounding formula

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

Step2: Convert the interest rate to decimal

Given $r = 4.5%=0.045$, $P = 1000$, and $t = 10$.

Step3: Substitute values into the formula

$A=1000\times e^{0.045\times10}$.

Step4: Calculate the exponent

$0.045\times10 = 0.45$. So $A = 1000\times e^{0.45}$.

Step5: Evaluate $e^{0.45}$ and find $A$

Using a calculator, $e^{0.45}\approx1.568312$. Then $A = 1000\times1.568312=1568.312$.

Step6: Round to the nearest penny

Rounding $1568.312$ to the nearest penny gives $A\approx1568.31$.

Answer:

$1568.31$