Question : Rahul invested equal sums of money at compound interest under two schemes A and B. Under scheme A, the interest rate was 10% per annum, and under scheme B, the interest rate was 12% pa. The compound interest after two years on the sum invested in scheme A was INR 1,050. How much is the interest earned under scheme B after two years, if the interest is compounded annually in both schemes?
Option 1: INR 1,722
Option 2: INR 1,270
Option 3: INR 1,272
Option 4: INR 1,372
Correct Answer: INR 1,272
Solution :
Given: Rahul invested equal sums of money at compound interest under two schemes A and B.
Under scheme A, the interest rate was 10% per annum, and under scheme B, the interest rate was 12% pa.
The compound interest after two years on the sum invested in scheme A was INR 1,050.
Use the formula, $A=P[1+\frac{R}{100}]^T$ where $A$, $P$, $R$ and $T$ are the amount, principal, rate, and number of years.
Let the sum be INR $P$.
The interest in scheme A is given as,
⇒ $2P(\frac{10}{100})+P(\frac{10}{100})^2=1050$
⇒ $\frac{2P}{10}+\frac{P}{100}=1050$
⇒ $\frac{20P+P}{100}=1050$
⇒ $21P=105000$
⇒ $P=$ INR 5,000
The interest in scheme B is given as,
= $2\times 5000 \times \frac{12}{100}+5000 \times (\frac{12}{100})^2$
= 1200 + 72
= INR 1,272
Hence, the correct answer is INR 1,272.
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