Question

For the same principal amount, the compound interest for two years at 5% per annum exceeds the simple interest for three years at 3% per annum by Rs 1125. Then the principal amount in rupees is ?
[This Question was asked as TITA]

• A. Rs. 60000
• B. Rs. 70000
• C. Rs. 100000
• D. Rs. 90000

Answer 1

The Correct Option is D

The principal amount is determined by calculating the difference between compound interest (CI) and simple interest (SI), which is given as Rs 1125. The formula for compound interest compounded annually is \( A = P(1+\frac{r}{100})^n \), and for simple interest is \( A = P + \frac{P \times r \times t}{100} \). For CI, with a 5% annual interest rate over 2 years: \( A_{CI} = P \left(1 + \frac{5}{100}\right)^2 = P \left(1.05\right)^2 = 1.1025P \). The compound interest is \( CI = A_{CI} - P = 1.1025P - P = 0.1025P \). For SI over three years at a 3% annual rate: \( A_{SI} = P + \frac{P \times 3 \times 3}{100} = P + 0.09P = 1.09P \). The simple interest is \( SI = A_{SI} - P = 0.09P \). The problem states that \( 0.1025P - 0.09P = 1125 \). This simplifies to: \[ 0.0125P = 1125 \] Solving for \( P \): \[ P = \frac{1125}{0.0125} = 90000 \] The principal amount is Rs 90000.