Question

grace opened a savings account and deposited $8,000.00 as principal. the account earns 5% interest, compounded quarterly. what is the balance after 4 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

$P = 8000$, $r = 0.05$, $n = 4$, $t = 4$

Step2: Calculate $nt$ value

$nt = 4 \times 4 = 16$

Step3: Calculate $\frac{r}{n}$ value

$\frac{r}{n} = \frac{0.05}{4} = 0.0125$

Step4: Calculate $(1+\frac{r}{n})^{nt}$

$(1 + 0.0125)^{16} = (1.0125)^{16} \approx 1.2198895$

Step5: Compute final balance $A$

$A = 8000 \times 1.2198895$

Answer:

$\$9759.12$