Question

ethan invested $720 in an account paying an interest rate of 3.6% compounded continuously. assuming no deposits or withdrawals are made, how much money, to the nearest hundred dollars, would be in the account after 10 years?

Explanation:

Step1: Recall continuous compound formula

The formula for continuous compounding is $A = Pe^{rt}$, where:

• $P$ = principal amount,
• $r$ = annual interest rate (decimal),
• $t$ = time in years,
• $A$ = final amount.

Step2: Convert rate to decimal

$r = \frac{3.6}{100} = 0.036$

Step3: Substitute values into formula

Substitute $P=720$, $r=0.036$, $t=10$:
$A = 720e^{(0.036 \times 10)}$

Step4: Simplify exponent

Calculate $0.036 \times 10 = 0.36$, so:
$A = 720e^{0.36}$

Step5: Calculate final value

First, $e^{0.36} \approx 1.4333$. Then:
$A \approx 720 \times 1.4333 \approx 1031.98$

Step6: Round to nearest hundred

$1031.98$ rounded to the nearest hundred is $1000$.

Answer:

$\$1000$