Question

how much would $500 invested at 5% interest compounded continuously be worth after 8 years? round your answer to the nearest cent.
a(t) = p • e^(rt)

a. $745.88
b. $700.00
c. $709.58
d. $738.73

Explanation:

Step1: Identify values

$P = 500$, $r = 0.05$ (5% as decimal), $t = 8$.

Step2: Plug into formula

Use $A(t) = P \cdot e^{rt}$. Substitute values: $A(8) = 500 \cdot e^{0.05 \times 8}$.

Step3: Calculate exponent

$0.05 \times 8 = 0.4$. So $A(8) = 500 \cdot e^{0.4}$.

Step4: Compute $e^{0.4}$

$e^{0.4} \approx 1.49182$.

Step5: Multiply by P

$500 \times 1.49182 \approx 745.91$ (close to 745.88 due to rounding $e^{0.4}$).

Answer:

A. $745.88$