Question

Ashok borrowed rs 12000 at some rate percent
Compound interest. After a year, he paid back rs 4000. If compound interest for the second year be rs 920 find:
1) The rate of interest charged
2) the amount of debt at the end of the second year

Answer 1

Loan = Rs 12,000    Interest rate = r % compound

Amount after one year = Rs 12,000 ( 1 + r/100) = Rs 120 (100+r)
Amount paid back after one year = Rs 4,000
Balance Amount in the loan = Rs 120 (100+r) - 4,000 = Rs (8,000 + 120 r)

Compound Interest for 2nd year turns out to be same as simple interest on the above amount:  $Rs\ (8000+ 120 r) * r / 100 = Rs\ 80\ r +1.2 r^2 \\ \\1.2\ r^2 + 80\ r = 920 \\ \\ r = \frac{-80 +- \sqrt{80^2+4*920*1.2}}{1.2 * 2} \\ \\ r = (-80+104)/2.4 = 10$

 Rate of interest is 10%           (we ignore the negative root of quadratic equation)

2)

$Amount\ after\ 2\ years : Rs (8,000 + 120 r ) + Rs (80 r + 1.2 r^2) \\ \\ = Rs 8,000+ 200 r + 1.2 r^2 \\ \\ = Rs\ 8,000 + 200*10+1.2*100 = Rs\ 11,200.$