Question

question
jaxon invested $370 in an account paying an interest rate of 2.6% compounded continuously. assuming no deposits or withdrawals are made, how much money, to the nearest ten dollars, would be in the account after 13 years?
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$
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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

$r = \frac{2.6}{100} = 0.026$

Step3: Plug values into formula

Substitute $P=370$, $r=0.026$, $t=13$:
$A = 370e^{(0.026 \times 13)}$

Step4: Calculate exponent first

$0.026 \times 13 = 0.338$

Step5: Compute exponential term

$e^{0.338} \approx 1.402$

Step6: Find final amount

$A \approx 370 \times 1.402 = 518.74$

Step7: Round to nearest ten dollars

$518.74$ rounded to the nearest ten is $520$

Answer:

$\$520$