Question

sarah opened a savings account and deposited $500.00 as principal. the account earns 11% interest, compounded quarterly. what is the balance after 6 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

$P = 500$, $r = 0.11$, $n = 4$, $t = 6$

Step2: Calculate exponent $nt$

$nt = 4 \times 6 = 24$

Step3: Calculate periodic rate $\frac{r}{n}$

$\frac{r}{n} = \frac{0.11}{4} = 0.0275$

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

$(1 + 0.0275)^{24} \approx 1.9330$

Step5: Compute final balance $A$

$A = 500 \times 1.9330$

Answer:

$966.50$