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\displaystyle 216:127. The rate of interest is:

Options

A0.1777\displaystyle 0.1777
B0.1567\displaystyle 0.1567
C0.1666\displaystyle 0.1666
D0.1587\displaystyle 0.1587
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Correct Answer

Option c0.1666\displaystyle 0.1666

All Options:

  • A0.1777\displaystyle 0.1777
  • B0.1567\displaystyle 0.1567
  • C0.1666\displaystyle 0.1666
  • D0.1587\displaystyle 0.1587

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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\displaystyle 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)3\frac{343}{216} = (1 + r)^3 **Step 3: Solve for r\displaystyle r** Observe that 343=73\displaystyle 343 = 7^3 and 216=63\displaystyle 216 = 6^3: (76)3=(1+r)3\left(\frac{7}{6}\right)^3 = (1 + r)^3 1+r=761 + r = \frac{7}{6} r=761=160.1666 (or 16.66%)r = \frac{7}{6} - 1 = \frac{1}{6} \approx 0.1666 \text{ (or } 16.66\%\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

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