camille opened a savings account and deposited $400.00 as principal. the account earns 15% interest…

camille opened a savings account and deposited $400.00 as principal. the account earns 15% interest, compounded continuously. what is the balance after 3 years? use the formula $a = pe^{rt}$, where $a$ is the balance (final amount), $p$ is the principal (starting amount), $e$ is the base of natural logarithms ($approx2.71828$), $r$ is the interest rate expressed as a decimal, and $t$ is the time in years. round your answer to the nearest cent.

camille opened a savings account and deposited $400.00 as principal. the account earns 15% interest, compounded continuously. what is the balance after 3 years? use the formula $a = pe^{rt}$, where $a$ is the balance (final amount), $p$ is the principal (starting amount), $e$ is the base of natural logarithms ($approx2.71828$), $r$ is the interest rate expressed as a decimal, and $t$ is the time in years. round your answer to the nearest cent.

Answer

Explanation:

Step1: Identify values

$P = 400$, $r=0.15$, $t = 3$

Step2: Substitute into formula

$A=Pe^{rt}=400\times e^{0.15\times3}$

Step3: Calculate exponent

$0.15\times3 = 0.45$

Step4: Find $e^{0.45}$

$e^{0.45}\approx1.568312$

Step5: Calculate final amount

$A = 400\times1.568312=627.3248\approx627.32$

Answer:

$627.32$