Answer to Question #306621 in Financial Math for Ndi

Question

A loan will be paid by means of payment of 250 each,every 6 months for 10 years.An interest rate of 5% per year compounded every 6 months will be applicable the present value of the loan is

Answer 1

Solution

Consider,

$A$ – The payment per period.

$P$ – The principal amount (loan taken).

$r$ – The interest rate per year,

$n$ – The number of times, the amount is compounded per annum, and

$t$ – The number of years,

we can write the formula, as 

${\color{Blue} P=A\times\frac{(1+\frac{r}{n})^{nt}-1}{(\frac{r}{n})(1+\frac{r}{n})^{nt}}}$

Replacing the values,

$A = 250$ ,        $r = 5\%$ ,            $n = 2$ (compounded every six months), $t = 10$ years

${\color{Red} P=(250)\times\frac{(1+\frac{0.05}{2})^{(2)(10)}-1}{(\frac{0.05}{2})(1+\frac{0.05}{2})^{(2)(10)}}}$

$P=3897.290572\$

Hence the loan amount to be paid will be

$P=3897.290572\$