Mathematics of FinancePYQ May 25Question 4011 of 507
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There is 60% increase in amount in 6 years at simple interest. What will be the compound interest of ₹ 12,000 after three years at the same rate?

Options

A₹ 2,160
B₹ 3,120
C₹ 3,972
D₹ 6,240
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Correct Answer

✅ Option c — ₹ 3,972

All Options:

  • A₹ 2,160
  • B₹ 3,120
  • C₹ 3,972
  • D₹ 6,240

Detailed Solution & Explanation

Let the principal amount be P\displaystyle P and the simple interest rate be R%\displaystyle R\%.
We are given that the simple interest increases the amount by 60%\displaystyle 60\% in 6\displaystyle 6 years. This means the interest (SI\displaystyle SI) earned is 60%\displaystyle 60\% of P\displaystyle P:
SI=0.60PSI = 0.60P
Using the simple interest formula SI=P×R×T100\displaystyle SI = \frac{P \times R \times T}{100} with T=6\displaystyle T = 6 years:
0.60P=P×R×61000.60P = \frac{P \times R \times 6}{100}
0.60=6R1000.60 = \frac{6R}{100}
6R=60  ⟹  R=10%6R = 60 \implies R = 10\%
So the annual rate of interest is 10%\displaystyle 10\%.

Now, we need to calculate the compound interest of ₹12,000\displaystyle ₹ 12,000 after 3\displaystyle 3 years at the same rate of 10%\displaystyle 10\% per annum compounded annually.
The formula for compound interest (CI\displaystyle CI) is:
CI=P[(1+R100)T−1]CI = P \left[\left(1 + \frac{R}{100}\right)^T - 1\right]
Substitute P=12000\displaystyle P = 12000, R=10\displaystyle R = 10, and T=3\displaystyle T = 3 into the formula:
CI=12000[(1+10100)3−1]CI = 12000 \left[\left(1 + \frac{10}{100}\right)^3 - 1\right]CI=12000[(1.1)3−1]CI = 12000 \left[(1.1)^3 - 1\right]
CI=12000[1.331−1]CI = 12000 \left[1.331 - 1\right]
CI=12000×0.331=3972CI = 12000 \times 0.331 = 3972
Therefore, the compound interest is ₹3,972\displaystyle ₹ 3,972.
Hence, **Option C** is the correct answer.

About This Chapter: Mathematics of Finance

Paper

Paper 3: Quantitative Aptitude

Weightage

12-16 Marks

Key Topics

Simple & Compound Interest, Annuity, Perpetuity

The most important mathematical chapter in the entire syllabus. It covers Simple Interest (SI), Compound Interest (CI), Nominal vs Effective rates, Present and Future Value, Annuities (Ordinary and Due), Sinking Funds, and Perpetuities. The concepts learned here are applied heavily in CA Intermediate and Final.

View Official ICAI Syllabus

Exam Strategy Tip

Guaranteed 12-16 marks. Master your calculator! Learn the 'GT' and compound interest M+/M- tricks to solve annuity questions in 10 seconds without writing long formulas.

Key Concepts to Understand

Compound Interest

Interest calculated on the initial principal, which also includes all of the accumulated interest of previous periods.

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If Rs. 1,000\displaystyle \text{Rs. }1,000 be invested at interest rate of 5%\displaystyle 5\% and the interest be added to the principal every 10\displaystyle 10 years, then the number in years in which it will amount to Rs. 2,000\displaystyle \text{Rs. }2,000 is:

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