# A payment of 1500$is due in three months.Find the equivalent value at nine months if the interest rate is 4% select one a:$1500 b:$1530 c:$1560 d:$1470 hexacordoK 2021-02-02 Answered A payment of 1500$ is due in three months.Find the equivalent value at nine months if the interest rate is 4%
select one
a:$1500 b:$1530
c:$1560 d:$1470
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stuth1

Given interest rate is 4% compounded quarterly
$F.V=P.V\left(1+\frac{r}{k}{\right)}^{nk}$
$F.V=$Future value
$P.V=$ Present value
$r=$rate of interest
$k=$number of times compounded per year
$n=$number of years
steps:
$r=4$
$k=4$(since compounded quarterly)

$nk=\frac{4}{4}=1$
substitute values in the above equation
$P.V=1500\left(1+\left(\frac{0.04}{4}\right)\right)$
$=1485.5$
Find the equivalent value
$r=4$
$k=4$(since compounded quarterly)
$n=9$ months=$\frac{9}{12}$
P.V $=1485.15$
$F.V=P.V\left(1+\left(\frac{r}{k}{\right)}^{nk}\right)$
$F.V=1485.5\left(1+\left(\frac{0.04}{4}{\right)}^{\frac{9}{12}4}$
$=1530.15$
Option B is correct