Question

doug puts $600.00 into an account to use for school expenses. the account earns 13% interest, compounded monthly. how much will be in the account after 5 years? use the formula $a = p\left(1 + \frac{r}{n}\
ight)^{nt}$, where $a$ is the balance (final amount), $p$ is the principal (starting amount), $r$ is the interest rate expressed as a decimal, $n$ is the number of times per year that the interest is compounded, and $t$ is the time in years. round your answer to the nearest cent.

Explanation:

Step1: Identify given values

$P = 600$, $r = 0.13$, $n = 12$, $t = 5$

Step2: Calculate monthly rate + 1

$\frac{r}{n} + 1 = \frac{0.13}{12} + 1 \approx 1.010833$

Step3: Calculate total compound periods

$nt = 12 \times 5 = 60$

Step4: Compute final amount

$A = 600 \times (1.010833)^{60}$
$A \approx 600 \times 1.900163$
$A \approx 1140.10$

Answer:

$\$1140.10$