Simple Interest and Compound Interest Question 1 - CAT 2020
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:
Step-by-Step Explanation
Let the principal amount be P.
Instead of setting up long-form equations, we can look at the effective interest percentages relative to the principal:
- Effective Compound Interest (CI) rate for 2 years at 5% per annum:
Using the successive percentage formula a + b + ab / 100:
Effective CI Rate = 5 + 5 + (5 × 5) / 100 = 10.25%
CI Earned = 10.25% of P
- Effective Simple Interest (SI) rate for 3 years at 3% per annum:
Effective SI Rate = 3 × 3 = 9%
SI Earned = 9% of P
- Equate the difference:
We are given that the compound interest exceeds the simple interest by Rs. 1125:
10.25% of P − 9% of P = 1125
1.25% of P = 1125
1.25 / 100 × P = 1125
P = (1125 × 100) / 1.25 = 90000
The principal amount is Rs. 90000.
Correct Answer: 90000
💡 FundaMakers Tip:
Bypassing standard interest formulas in favor of Net Effective Percentage simplifies comparison problems. Converting compound interest rates to a net single percentage (like 10.25%) turns a multi-tier problem into a simple linear step.