Simple Interest and Compound Interest Question 2 - CAT 2020
A person invested a certain amount of money at 10% annual interest, compounded half-yearly. After one and a half years, the interest and principal together became Rs. 18522. The amount, in rupees, that the person had invested is:
Step-by-Step Explanation
- Determine the rate and compounding periods:
The nominal annual interest rate is 10%, compounded half-yearly.
○ Half-yearly interest rate = 10% / 2 = 5%
○ Total time = 1.5 years, which contains 1.5 × 2 = 3 half-yearly compounding periods.
- Set up the amount formula:
Let the initial investment be P. The total maturity value accumulated after 3 periods is Rs. 18522:
A = P × (1 + 5 / 100)³
18522 = P × (1.05)³
- Convert decimals to fractions for faster calculation:
1.05 = 105 / 100 = 21 / 20
18522 = P × (21 / 20)³
18522 = P × 9261 / 8000
- Isolate P:
Notice that 18522 is exactly double of 9261 (9261 × 2 = 18522).
2 = P / 8000 ⇒ P = 2 × 8000 = 16000
The amount invested was Rs. 16000.
Correct Answer: 16000
💡 FundaMakers Tip:
Decimal multiplications like (1.05)³ waste precious time during the exam. Convert percentages into standard fractions early on. Recognizing that 5% = 1 / 20 turns the multiplier into 21 / 20. Knowing common cubes up to 30 helps you spot that 21³ = 9261, which cancels out cleanly with the given question value.