Question

levi invested $370 in an account paying an interest rate of 6.9% compounded continuously. assuming no deposits or withdrawals are made, how much money, to the nearest ten dollars, would be in the account after 13 years?

Explanation:

Step1: Define continuous compound formula

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

• $P$ = principal amount,
• $r$ = annual interest rate,
• $t$ = time in years,
• $e$ = Euler's number ($\approx2.71828$)

Step2: Substitute given values

Substitute $P=370$, $r=0.069$, $t=13$:
$A = 370 \times e^{0.069 \times 13}$

Step3: Calculate exponent term

First compute $0.069 \times 13 = 0.897$, so:
$A = 370 \times e^{0.897}$
$e^{0.897} \approx 2.452$

Step4: Compute final amount

$A = 370 \times 2.452 \approx 907.24$

Step5: Round to nearest ten dollars

Round $907.24$ to the nearest ten: $910$

Answer:

$\$910$