Mathematics of FinanceMCQPYQ Jan 21Question 1220 of 512
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A sum of money is lent at C.I. rate $20\%p.a.\displaystyle p.a.2$ years. It would fetch $482$ more if the interest is compounded half yearly. The sum is:

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

✅ Option c — $20,000$

All Options:

  • A$19,800$
  • B$19,900$
  • C$20,000$
  • D$20,100$

Detailed Solution & Explanation

**Derivation of Principal Amount** Given: - Rate of Interest (r\displaystyle r) = $20\%$ per annum - Time (t\displaystyle t) = 2\displaystyle 2 years - Interest difference between compounding half-yearly and annually = Rs. 482\displaystyle Rs. \displaystyle \text{Rs. }482 **Step 1: Calculate Compound Interest when compounded annually (CIa\displaystyle CI_a)** Aa=P(1+r)t=P(1+0.20)2=1.44PA_a = P(1 + r)^t = P(1 + 0.20)^2 = 1.44 P CIa=Aa−P=0.44PCI_a = A_a - P = 0.44 P **Step 2: Calculate Compound Interest when compounded half-yearly (CIh\displaystyle CI_h)** - Periodic rate i=20%2=10%=0.10\displaystyle i = 20%2=10\displaystyle \frac{20\%}{2} = 10\% = 0.10 - Number of periods n=2×2=4\displaystyle n = 2 ×\displaystyle \times 2 = 4 Ah=P(1+i)n=P(1.10)4=1.4641PA_h = P(1 + i)^n = P(1.10)^4 = 1.4641 P CIh=Ah−P=0.4641PCI_h = A_h - P = 0.4641 P **Step 3: Set up the difference equation and solve for P\displaystyle P** CIh−CIa=482CI_h - CI_a = 482 0.4641P−0.44P=4820.4641 P - 0.44 P = 482 0.0241P=4820.0241 P = 482 P=4820.0241=Rs. 20,000P = \displaystyle \frac{482}{0.0241} = \text{Rs. }20,000 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.

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