Question : Raja borrowed INR 15,000 on simple interest at the rate of 13% per annum and lent it on compound interest at the rate of 15% per annum, compounded annually. What is Raja's gain in two years?
Option 1: INR 1,080.00
Option 2: INR 1,125.00
Option 3: INR 937.50
Option 4: INR 865.50
Correct Answer: INR 937.50
Solution :
Given: Raja borrowed INR 15,000 on simple interest at the rate of 13% per annum and lent it on compound interest at the rate of 15% per annum, compounded annually.
We know, Simple interest = $\frac{\text{Principal × Rate × Time}}{100}=\frac{15000\times 13\times 2}{100}=$ INR 3,900
We know, $\text{Total Amount}=\text{Principal}×(1+\frac{\text{Rate}}{100})^{\text{Time}}$
$⇒\text{Total Amount}=15000×[1+\frac{15}{100}]^2$
$⇒ \text{Total Amount}=15000\times \frac{529}{400}=$ INR 19837.50
Compound interest $=19837.50-15000=$ INR 4,837.50
Raja's gain in two years = 4837.50 – 3900 = INR 937.50
Hence, the correct answer is INR 937.50.
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