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

Options

A19,800\displaystyle 19,800
B19,900\displaystyle 19,900
C20,000\displaystyle 20,000
D20,100\displaystyle 20,100
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Correct Answer

Option c20,000\displaystyle 20,000

All Options:

  • A19,800\displaystyle 19,800
  • B19,900\displaystyle 19,900
  • C20,000\displaystyle 20,000
  • D20,100\displaystyle 20,100

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Detailed Solution & Explanation

**Derivation of Principal Amount** Given: - Rate of Interest (r\displaystyle r) = 20%\displaystyle 20\% per annum - Time (t\displaystyle t) = 2\displaystyle 2 years - Interest difference between compounding half-yearly and annually = Rs. 482\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=AaP=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 = \frac{20\%}{2} = 10\% = 0.10 - Number of periods n=2×2=4\displaystyle n = 2 \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=AhP=0.4641PCI_h = A_h - P = 0.4641 P **Step 3: Set up the difference equation and solve for P\displaystyle P** CIhCIa=482CI_h - CI_a = 482 0.4641P0.44P=4820.4641 P - 0.44 P = 482 0.0241P=4820.0241 P = 482 P=4820.0241=Rs. 20,000P = \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

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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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