A man borrows ₹ 4000 at 15\% compound rate of interest. At the end of each year he pays back ₹ 1500. How much amount should be pay at the end of the third year to clear all his dues?
(a)₹ 874.75
(b)₹ 824.50
(c)₹ 924.25
(d)₹ 974.25
Answer
Answer (as printed): A
Explanation
Amount after 1st year $=₹\left[4000\left(1+\frac{15}{100}\right)-1500\right]$ $$\begin{aligned} & =₹\left[\left(4000 \times \frac{23}{20}\right)-1500\right] \\ & =₹(4600-1500)=₹ 3100 . \end{aligned}$$ Amount after 2nd year $=₹\left[3100\left(1+\frac{15}{100}\right)-1500\right]$ $$\begin{aligned} & =₹\left[\left(3100 \times \frac{23}{20}\right)-1500\right] \\ & =₹(3565-1500)=₹ 2065 . \end{aligned}$$ Amount after 3 rd year $=₹\left[2065\left(1+\frac{15}{100}\right)-1500\right]$ $$\begin{aligned} & =₹\left[\left(2065 \times \frac{23}{20}\right)-1500\right] \\ & =₹(2374.75-1500)=₹ 874.75 . \end{aligned}$$
Explanation as extracted from the printed page; notation may be imperfect.