Question : A sum of Rs. 210 was taken as a loan. This is to be paid back in two equal installments. If the rate of interest is 10% compounded annually, then the value of each installment is:
Option 1: Rs. 127
Option 2: Rs. 121
Option 3: Rs. 210
Option 4: Rs. 225
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Correct Answer: Rs. 121
Solution :
Let $x$ be the equal instalment at the end of one year.
In the first year,
Sum, $P$ = Rs. 210
Interest = $\frac{PnR}{100}$
Interest at the end of one year at a 10% rate of interest = 210 × 0.1 = 21
At the beginning of the second year after paying '$x$',
The sum for the second year becomes $P = 210+21-x$
⇒ $P = 231 - x$
Interest at the end of the second year at 10% rate of interest $= (231-x) × 0.1 = 23.1-0.1x$
Now, total instalment = Amount taken as loan + Interest for the first year + Interest of second year
So, the total instalment, $2x = 210+21+23.1–0.1x$
⇒ $x = \frac{254.1}{2.1}$
⇒ $x = 121$
Hence, the correct answer is Rs. 121.
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