Mathematics of FinanceMCQPYQ May 20Question 1305 of 512
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The effective rate of interest corresponding to a nominal rate 3%\displaystyle 3\% p.a payable half yearly is

Options

A3.2%\displaystyle 3.2\% p.a
B3.25%\displaystyle 3.25\% p.a
C3.0225%\displaystyle 3.0225\% p.a
Dnone of these
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Correct Answer

✅ Option c — 3.0225%\displaystyle 3.0225\% p.a

All Options:

  • A3.2%\displaystyle 3.2\% p.a
  • B3.25%\displaystyle 3.25\% p.a
  • C3.0225%\displaystyle 3.0225\% p.a
  • Dnone of these

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Detailed Solution & Explanation

**Derivation of Effective Rate of Interest** Given: - Nominal rate of interest (r\displaystyle r) = 3%\displaystyle 3\% per annum - Compounding Frequency = Half-yearly (m=2\displaystyle m = 2) **Step 1: Calculate the periodic rate (i\displaystyle i)** i=rm=3%2=1.5%=0.015 per half-yeari = \frac{r}{m} = \frac{3\%}{2} = 1.5\% = 0.015 \text{ per half-year} **Step 2: Calculate the effective annual interest rate (E\displaystyle E)** E=(1+i)m−1E = (1 + i)^m - 1 E=(1+0.015)2−1E = (1 + 0.015)^2 - 1 E=(1.015)2−1E = (1.015)^2 - 1 E=1.030225−1=0.030225 or 3.0225% p.a.E = 1.030225 - 1 = 0.030225 \text{ or } 3.0225\% \text{ p.a.} 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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A certain sum of money was put at S.I. for 2.5\displaystyle 2.5 years at a certain rate of S.I. p.a. Had it been put at 4%\displaystyle 4\% higher rate, it would have fetched 500\displaystyle 500 more. Find the sum of money.

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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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