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

Question

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

Answer 1

Given interest rate is 4% compounded quarterly
$F . V = P . V (1 + \frac{r}{k})^{n k}$
$F . V =$ 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)
$n = 3 m o n t h s = \frac{3}{12} y e a r s = (\frac{1}{4}) y e a r s$
$n k = \frac{4}{4} = 1$
substitute values in the above equation
$P . V = 1500 (1 + (\frac{0.04}{4}))$
$= 1485.5$
Find the equivalent value
$r = 4$
$k = 4$ (since compounded quarterly)
$n = 9$ months= $\frac{9}{12}$
P.V $= $ 1485.15$
$F . V = P . V (1 + (\frac{r}{k})^{n k})$
$F . V = 1485.5 (1 + (\frac{0.04}{4})^{\frac{9}{12} 4}$
$= $ 1530.15$
Option B is correct

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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