Mathematics of FinanceMCQPYQ Nov 19Question 1199 of 512
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Find the effective rate of interest at 10%\displaystyle 10\% p.a. which interest is payable quarterly

Options

A10.38%\displaystyle 10.38\%
B5%\displaystyle 5\%
C5.04%\displaystyle 5.04\%
D4%\displaystyle 4\%
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Correct Answer

✅ Option a — 10.38%\displaystyle 10.38\%

All Options:

  • A10.38%\displaystyle 10.38\%
  • B5%\displaystyle 5\%
  • C5.04%\displaystyle 5.04\%
  • D4%\displaystyle 4\%

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Detailed Solution & Explanation

**Derivation of Effective Rate of Interest** Given: - Nominal Rate (r\displaystyle r) = 10%\displaystyle 10\% per annum - Compounding Frequency = Quarterly (m=4\displaystyle m = 4) **Step 1: Find periodic interest rate (i\displaystyle i)** i=rm=10%4=2.5%=0.025 per periodi = \frac{r}{m} = \frac{10\%}{4} = 2.5\% = 0.025 \text{ per period} **Step 2: Calculate the effective rate of interest (E\displaystyle E)** E=(1+i)m−1E = (1 + i)^m - 1 E=(1+0.025)4−1E = (1 + 0.025)^4 - 1 E=(1.025)4−1E = (1.025)^4 - 1 **Step 3: Calculate the value** (1.025)4≈1.103813(1.025)^4 \approx 1.103813 E=1.103813−1=0.103813 or 10.38%E = 1.103813 - 1 = 0.103813 \text{ or } 10.38\% Hence, **Option A** 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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