Question

anita opened a savings account and deposited $300.00. the account earns 13% interest, compounded quarterly. if she wants to use the money to buy a new bicycle in 2 years, how much will she be able to spend on the bike? 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

$P = 300$, $r = 0.13$, $n = 4$, $t = 2$

Step2: Calculate periodic rate

$\frac{r}{n} = \frac{0.13}{4} = 0.0325$

Step3: Calculate total compounding periods

$nt = 4 \times 2 = 8$

Step4: Compute growth factor

$(1 + 0.0325)^8 = (1.0325)^8 \approx 1.29157$

Step5: Calculate final amount

$A = 300 \times 1.29157$

Answer:

$387.47$