Question

Mr. Nirav borrowed rupees Rs. $50,000$ from the bank for $5$ years. The rate of interest is $9\%$ per annum compounded monthly. Find the payment he makes monthly if he pays back at the beginning of each month.

Answer 1

Applying for an annuity due when payments are made at the beginning of each month
Here, $P=50,000,i=\frac{9}{100}=0.09$
$P=\frac{12a}{i}\left(\begin{array}{c}1+\frac{i}{12}\end{array}\right)\left|\begin{array}{c}1-{\left(\begin{array}{c}1+\frac{i}{12}\end{array}\right)}^{-12n}\end{array}\right|$

$50,000=\frac{a}{0.0075}(1+0.0075)[1-(1-0075{)}^{-60}]$

$\Rightarrow 375=a\left(1.0075\right)(1-[1.0075{]}^{-60})$

$\Rightarrow 375=a[1.0075-(1.0075{)}^{-59}]$ ...(i)

Let $x=(1.075{)}^{-59}$
$\Rightarrow \log x=-59\log \left(1.0075\right)$
$=-59\times 0.0032$
$=-0.1914$
$=\overline{1}.8085$
$\therefore x=\text{antilog}\left(\overline{1}.8085\right)$
$=0.6434$

From (i), $375=a(1.0075-0.6434)$
$375=a\left(0.3641\right)$
$a=\frac{375}{0.3641}$
$a=1029.94$

Hence, the payment Mr. Nirav makes monthly is Rs. $1029.94$.