Question

dirk puts $700.00 into an account to use for school expenses. the account earns 3% interest, compounded quarterly. how much will be 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.

Explanation:

Step1: Identify given values

$P = 700$, $r = 0.03$, $n = 4$, $t = 8$

Step2: Calculate exponent $nt$

$nt = 4 \times 8 = 32$

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

$\frac{r}{n} = \frac{0.03}{4} = 0.0075$

Step4: Calculate growth factor $1+\frac{r}{n}$

$1 + 0.0075 = 1.0075$

Step5: Compute compound amount $A$

$A = 700 \times (1.0075)^{32}$
First calculate $(1.0075)^{32} \approx 1.270111$
Then $A = 700 \times 1.270111 \approx 889.08$

Answer:

$\$889.08$