Question

mason puts $9,016.00 into an account to use for school expenses. the account earns 8% interest, compounded monthly. how much will be in the account after 10 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

$P = 9016.00$, $r = 0.08$, $n = 12$, $t = 10$

Step2: Calculate exponent term

$nt = 12 \times 10 = 120$

Step3: Calculate monthly rate

$\frac{r}{n} = \frac{0.08}{12} \approx 0.006667$

Step4: Calculate growth factor

$1 + \frac{r}{n} = 1 + 0.006667 = 1.006667$

Step5: Compute compounded amount

$A = 9016.00 \times (1.006667)^{120}$
$(1.006667)^{120} \approx 2.21964$
$A = 9016.00 \times 2.21964 \approx 20012.27$

Answer:

$\$20012.27$