Mathematics of FinanceMCQPYQ Nov 20Question 1207 of 512
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A certain sum invested at 4%\displaystyle 4\% per annum compounded semi-annually amounts to 1,20,000\displaystyle 1,20,000 at the end of one year. Find the sum:

Options

A1,15,340\displaystyle 1,15,340
B1,10,120\displaystyle 1,10,120
C1,12,812\displaystyle 1,12,812
D1,13,113\displaystyle 1,13,113
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Correct Answer

✅ Option a — 1,15,340\displaystyle 1,15,340

All Options:

  • A1,15,340\displaystyle 1,15,340
  • B1,10,120\displaystyle 1,10,120
  • C1,12,812\displaystyle 1,12,812
  • D1,13,113\displaystyle 1,13,113

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Detailed Solution & Explanation

**Derivation of Principal Amount** Given: - Amount (A\displaystyle A) = Rs. 1,20,000\displaystyle \text{Rs. }1,20,000 - Rate of Interest (r\displaystyle r) = 4%\displaystyle 4\% per annum compounded semi-annually - Time (t\displaystyle t) = 1\displaystyle 1 year **Step 1: Calculate periodic rate (i\displaystyle i) and number of periods (n\displaystyle n)** - Periodic rate i=r2=4%2=2%=0.02\displaystyle i = \frac{r}{2} = \frac{4\%}{2} = 2\% = 0.02 per half-year. - Number of periods n=t×2=1×2=2\displaystyle n = t \times 2 = 1 \times 2 = 2 half-years. **Step 2: Calculate Principal (P\displaystyle P)** A=P(1+i)nA = P(1 + i)^n 120000=P(1+0.02)2120000 = P(1 + 0.02)^2 120000=P(1.02)2120000 = P(1.02)^2 120000=1.0404P120000 = 1.0404 P P=1200001.0404≈Rs. 1,15,340.25P = \frac{120000}{1.0404} \approx \text{Rs. }1,15,340.25 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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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.

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