9. suppose you invest $3500 into an account at an apr of 3.1% that compounds interest continuously. (a) find…

Explanation:

Step1: Identify the continuous - compounding 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 number of years.

Step2: Convert the percentage to decimal

The annual percentage rate (APR) $r = 3.1%=0.031$, the principal amount $P = 3500$, and the number of years $t = 5$.

Step3: Substitute values into the formula

Substitute $P = 3500$, $r=0.031$, and $t = 5$ into the formula $A = Pe^{rt}$. We get $A=3500\times e^{0.031\times5}$.

Step4: Calculate the exponent

First, calculate $0.031\times5 = 0.155$. Then, find the value of $e^{0.155}$. Using a calculator, $e^{0.155}\approx1.16798$.

Step5: Calculate the final amount

Multiply $3500$ by $1.16798$. So, $A = 3500\times1.16798=4087.93$.

Answer:

$4087.93$