Question

Ashok borrowed Rs.12,000 at some rate per cent compound interest. After a year, he paid back Rs. 4,000. If compound interest for the second year be Rs. 920, find :

(i) the rate of interest charged

(ii) the amount of debt at the end of the second year.

Answer 1

(i) Let x% be the rate of interest charged.

For 1^st year:

P = Rs.12,000, R = x% and T = 1
Interest (I)$=\frac{12000\times x\times 1}{100}=Rs.120x$
For 2${}^{nd}$ year:
After a year, Ashok paid back Rs. 4,000.
So, P=Rs.(12,000+120x-4000)=Rs.(8000+120x\)
$\Rightarrow \text{interest}=\frac{(8000+120x)\times 1\times x}{100}$
$\Rightarrow \text{interest}=80x+1.20x^2$
Given, the compound interest for the second year is Rs. 920.
$\Rightarrow 80x+1.20x^2=920$
$\Rightarrow 1.2x^2+80x-920=0$
$\Rightarrow 3x^2+200x-2300=0$
$\Rightarrow 3x^2+230x-30x-2300=0$
$\Rightarrow x(3x+230)-10(3x+230)=0$
$\Rightarrow (3x+230)(x-10)=0$
$\Rightarrow x=10$ and $x=\frac{-230}{3}$ is not possible as rate of interest can't be negative.
Therefore, the rate of interest charged is 10%.

(ii)

For 1^st year:

Interest = Rs.120x = Rs.1200

For 2^nd year:

Interest = Rs.(80x + 1.20x²)
$=80\left(10\right)+1.20(10{)}^2$
$=800+1.2\left(100\right)$
= Rs.920

The amount of debt at the end of the second year is equal to the addition of principal of the second year and interest for the two years.

Debt = Rs.8,000 + Rs.1200 + Rs.920 = Rs.10,120