Question

A customer deposits $2000 in a savings account that pays 5.2% interest compounded quarterly. How much money will the customer have in the account after 2 yr? After 5 yr?

Answer 1

To solve this we are going to use the compound interest formula: 
$A=P(1+ \frac{r}{n} )^{nt}$
where
$A$ is the amount after $t$ years 
$P$ is the initial amount 
$r$ is the interest rate in decimal form 
$n$ is the number of times the interest is compounded per year
$t$ is the time in years.

First, we are going to convert the interest rate to decimal form by divide the rate by 100%:
$\frac{5.2}{100} =0.052$
Next, we are going to find $n$. Since the interest is compounded quarterly, it is compounded 4 times per year, so.
$n=4$

1. For our problem we know that $t=2$ and $P=2000$. We also know for our previous calculations that $r=0.052$ and $n=4$. So lets replace those values in our compound interest formula to find $A$:
$A=P(1+ \frac{r}{n} )^{nt}$
$A=2000(1+ \frac{0.052}{4} )^{(2)(4)$
$A=2000(1+ \frac{0.052}{4})^{8}$
$A=2217.71$
We can conclude that after 2 years the customer will have $2,217.71 in his account.

2. We know for our problem that this time $t=5$, the initial investment remains the same, so $p=2000$, and we also know for our previous calculations that $r=0.052$ and $n=4$. So lets replace those values in our formula one more time:
$A=P(1+ \frac{r}{n} )^{nt}$
$A=2000(1+ \frac{0.052}{4} )^{(4)(5)$
$A=2000(1+ \frac{0.052}{4} )^{20}$
$A=2589.52$
We can conclude that after 5 years the customer will have $2,589.52 in his account.