Question

rudy and edna deposit $3,000.00 into a savings account which earns 3% interest compounded quarterly. they want to use the money in the account to go on a trip in 3 years. how much will they be able to spend? 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

$P = 3000$, $r = 0.03$, $t = 3$, $n = 4$

Step2: Calculate periodic rate & total periods

$\frac{r}{n} = \frac{0.03}{4} = 0.0075$, $nt = 4 \times 3 = 12$

Step3: Compute growth factor

$1 + \frac{r}{n} = 1 + 0.0075 = 1.0075$

Step4: Calculate final amount

$A = 3000 \times (1.0075)^{12}$
$(1.0075)^{12} \approx 1.093806897$
$A \approx 3000 \times 1.093806897 = 3281.420691$

Step5: Round to nearest cent

$A \approx 3281.42$

Answer:

$\$3281.42$