Question

Ashok borrowed ₹12,000 at some rate on compound interest. After a year, he paid back ₹4,000. If the compound interest for the second year is ₹920, find:
i. The rate of interest charged
ii. The amount of debt at the end of the second year

Answer 1

(i) Let’s assume x% to be the rate of interest charged
Then C.I, calculated
For 1st year
P = ₹12,000, R = x% and T = 1 year
Interest = $\frac{12,000\times x\times 1}{100}$ = 120x
And, amount = ₹(12,000 + 120x) $\left(0.5Mark\right)$
For 2nd year
After a year, given that Ashok paid back ₹4,000.
P = (₹12,000 + ₹120x) - ₹4,000 = ₹(8,000 + 120x)
Interest = $\frac{(8,000+120x)\times x\times 1}{100}$ = ₹(80x + 1.20$x^2$) $\left(0.5Mark\right)$
But given, the compound interest for the second year is ₹920
₹(80x + 1.20$x^2$) = ₹920
1.20$x^2$ + 80x - 920 = 0
3$x^2$ + 200x - 2300 = 0
3$x^2$ + 230x - 30x - 2300 = 0
x(3x + 230) -10(3x + 230) = 0
(3x + 230) (x - 10) = 0
x = $\frac{-230}{3}$ or x = 10 $\left(0.5Mark\right)$
Since, the rate of interest cannot be negative
So, x = 10 Therefore, the rate of interest charged is 10%.$\left(0.5Mark\right)$
(ii) For 1st year:
Interest = ₹120x = ₹1200 $\left(0.5Mark\right)$
For 2nd year: Interest = ₹(80x + 1.20$x^2$) = ₹920 $\left(0.5Mark\right)$
The amount of debt at the end of the second year is equal to the sum of the principal of the second year and interest for the two years.
Thus, Total debt = ₹(8,000 + 1,200 + 920) = ₹10,120$\left(1Mark\right)$