Mathematics of FinanceMCQPYQ Nov 20Question 1211 of 512
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The ratio of principal and the compound interest value for three years (compounded annually) is $216:127$. The rate of interest is:

Select Your Answer (Keyboard: A, B, C, D)
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Correct Answer

✅ Option c — $0.1666$

All Options:

  • A$0.1777$
  • B$0.1567$
  • C$0.1666$
  • D$0.1587$

Detailed Solution & Explanation

**Derivation of Rate of Interest from Principal and CI Ratio** Given: - Ratio of Principal (P\displaystyle P) to Compound Interest (CI\displaystyle CI) for 3\displaystyle 3 years = $216:127$ - Let P=216\displaystyle P = 216 and CI=127\displaystyle CI = 127. **Step 1: Calculate the future amount (A\displaystyle A)** A=P+CI=216+127=343A = P + CI = 216 + 127 = 343 **Step 2: Set up the Compound Interest Amount formula** A=P(1+r)tA = P(1 + r)^t 343=216(1+r)3343 = 216(1 + r)^3 343216=(1+r)3343216\displaystyle \frac{343}{216} = (1 + r)^3 **Step 3: Solve for r\displaystyle r** Observe that $343 = 7^3\displaystyle and $216 = 6^3: (76)3=(1+r)3\left(76\displaystyle \frac{7}{6}\right)^3 = (1 + r)^3 1+r=761 + r = 76\displaystyle \frac{7}{6} r=76−1=16≈0.1666 (or 16.66%)r = 76−1=16\displaystyle \frac{7}{6} - 1 = \frac{1}{6} ≈\displaystyle \approx 0.1666  (or \displaystyle \text{ (or } 16.66\%)\displaystyle \text{)} 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 Rs. \displaystyle \text{Rs. }1,000 be invested at interest rate of 5%\displaystyle 5\% and the interest be added to the principal every $10$ years, then the number in years in which it will amount to $Rs. \displaystyle \text{Rs. }2,000$ is:

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