Question

6.
Find the present value.
Amount Needed: $12,300
Time (Years): 4
Rate: 4%
Compounded: quarterly


$10,514.04

$11,820.05

$10,332.00

$10,489.69

Answer 1

To solve this we are going to use the formula for  future value: $FV=PV(1+ \frac{r}{n} )^{nt}$
where 
$FV$ is the future value 
$PV$ is the present value 
$r$ 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

We know for our problem that $FV=12300$, $r= \frac{4}{100} =0.04$, and $t=4$. Since the interest is compounded quarterly, it is compounded 4 times per year; therefore, $n=4$. Lets replace those values in our formula to find and solve for $PV$:
$FV=PV(1+ \frac{r}{n} )^{nt}$
$12300=PV(1+ \frac{0.04}{4} )^{(4)(4)}$
$PV= \frac{12300}{(1+ \frac{0.04}{4} )^{(4)(4)} }$
$PV=10489.70$

We can conclude that the present amount needed to have $12,300 after 4 years according to your given choices is $10,489.69