solve the problem. round to the nearest cent....
solve the problem. round to the nearest cent. jasons savings account has a balance of $2179. after 5 years, what will the amount of interest be at 6% compounded quarterly? a. $760.80 b. $65.37 c. $755.80 d. $746.80
Answer
# Explanation:
## Step1: Identify compound - interest formula
The compound - interest formula is $A = P(1+\frac{r}{n})^{nt}$, where $P$ is the principal amount, $r$ is the annual interest rate (in decimal form), $n$ is the number of times interest is compounded per year, and $t$ is the number of years. The interest $I=A - P$. Given $P = 2179$, $r=0.06$, $n = 4$ (compounded quarterly), and $t = 5$.
## Step2: Calculate the value of $(1+\frac{r}{n})^{nt}$
First, calculate $\frac{r}{n}=\frac{0.06}{4}=0.015$, and $nt=4\times5 = 20$. Then $(1+\frac{r}{n})^{nt}=(1 + 0.015)^{20}$. Using a calculator, $(1.015)^{20}\approx1.346855$.
## Step3: Calculate the amount $A$
$A=P(1+\frac{r}{n})^{nt}=2179\times1.346855\approx2925.80$.
## Step4: Calculate the interest $I$
$I=A - P=2925.80-2179 = 746.80$.
# Answer:
d. $\$746.80$