Mathematics of FinancePYQ Sept 25Question 4416 of 507
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The compound interest of ₹ 4,900 is ₹ 1661 for 2 years at a certain rate of interest, compounded annually. What is the rate of interest per annum in percentage?

Options

A19.71
B17.71
C13.71
D15.71
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Correct Answer

✅ Option d — 15.71

All Options:

  • A19.71
  • B17.71
  • C13.71
  • D15.71

Detailed Solution & Explanation

Given: Principal (P\displaystyle P) = ₹ 4,900 Compound Interest (CI\displaystyle CI) = ₹ 1,661 Time (n\displaystyle n) = 2 years
Let r\displaystyle r be the annual rate of interest. The compound amount (A\displaystyle A) is: A=P+CI=4,900+1,661=6,561 rupeesA = P + CI = 4,900 + 1,661 = 6,561\text{ rupees}
The compound interest formula for amount is: A=P(1+r)2A = P(1+r)^2 Substitute the values: 6,561=4,900(1+r)26,561 = 4,900(1+r)^2 (1+r)2=6,5614,900(1+r)^2 = \frac{6,561}{4,900}
Taking the square root on both sides: 1+r=6,5614,9001+r = \sqrt{\frac{6,561}{4,900}} We know that: 4,900=70and812=6,561  ⟹  6,561=81\sqrt{4,900} = 70 \quad \text{and} \quad 81^2 = 6,561 \implies \sqrt{6,561} = 81 So: 1+r=81701+r = \frac{81}{70} r=8170−1=1170≈0.15714r = \frac{81}{70} - 1 = \frac{11}{70} \approx 0.15714 In percentage: Rate=0.15714×100%≈15.71%\text{Rate} = 0.15714 \times 100\% \approx 15.71\%
Hence, **Option D** 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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