Question

wyatt is saving up money to buy a car. wyatt puts $5,423.00 into an account which earns 2% interest, compounded quarterly. how much will he have in the account after 8 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. $\square$

Explanation:

Step1: Identify given values

$P = 5423$, $r = 0.02$, $n = 4$, $t = 8$

Step2: Calculate exponent term

$nt = 4 \times 8 = 32$

Step3: Calculate periodic rate

$\frac{r}{n} = \frac{0.02}{4} = 0.005$

Step4: Calculate growth factor

$1 + 0.005 = 1.005$

Step5: Compute compound factor

$1.005^{32} \approx 1.173198$

Step6: Calculate final amount

$A = 5423 \times 1.173198$

Answer:

$6362.25$