Mathematics of FinanceMCQPYQ Nov 20Question 1206 of 512
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An amount P\displaystyle P becomes 5,100.5\displaystyle 5,100.5 and 5,203\displaystyle 5,203 after second and fourth years respectively at 1%\displaystyle 1\% of interest per annum compounded annually. This value of P\displaystyle P and R\displaystyle R are

Options

A4,000\displaystyle 4,000 and 1.5\displaystyle 1.5
B5,000\displaystyle 5,000 and 1\displaystyle 1
C6,000\displaystyle 6,000 and 2\displaystyle 2
D5,500\displaystyle 5,500 and 3\displaystyle 3
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Correct Answer

✅ Option b — 5,000\displaystyle 5,000 and 1\displaystyle 1

All Options:

  • A4,000\displaystyle 4,000 and 1.5\displaystyle 1.5
  • B5,000\displaystyle 5,000 and 1\displaystyle 1
  • C6,000\displaystyle 6,000 and 2\displaystyle 2
  • D5,500\displaystyle 5,500 and 3\displaystyle 3

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Detailed Solution & Explanation

**Derivation of Principal and Rate from Compound Interest Amounts** Given: - Amount after 2\displaystyle 2 years (A2\displaystyle A_2) = Rs. 5,100.50\displaystyle \text{Rs. }5,100.50 - Amount after 4\displaystyle 4 years (A4\displaystyle A_4) = Rs. 5,203.00\displaystyle \text{Rs. }5,203.00 - Compounded annually **Step 1: Express the amounts in terms of Principal (P\displaystyle P) and Rate (R\displaystyle R)** A2=P(1+i)2=5100.5A_2 = P(1 + i)^2 = 5100.5 A4=P(1+i)4=5203A_4 = P(1 + i)^4 = 5203 where i=R100\displaystyle i = \frac{R}{100} is the rate of interest in decimals. **Step 2: Divide the two equations to find (1+i)\displaystyle (1+i)** A4A2=P(1+i)4P(1+i)2\frac{A_4}{A_2} = \frac{P(1+i)^4}{P(1+i)^2} 52035100.5=(1+i)2\frac{5203}{5100.5} = (1+i)^2 1.020096=(1+i)21.020096 = (1+i)^2 Taking the square root of both sides: 1+i=1.020096=1.011+i = \sqrt{1.020096} = 1.01 i=0.01  ⟹  R=1% per annumi = 0.01 \implies R = 1\% \text{ per annum} **Step 3: Solve for Principal (P\displaystyle P)** Substitute 1+i=1.01\displaystyle 1+i = 1.01 back into the equation for A2\displaystyle A_2: 5100.5=P(1.01)25100.5 = P(1.01)^2 5100.5=1.0201P5100.5 = 1.0201 P P=5100.51.0201=Rs. 5,000P = \frac{5100.5}{1.0201} = \text{Rs. }5,000 So, P=Rs. 5,000\displaystyle P = \text{Rs. }5,000 and R=1%\displaystyle R = 1\%. Hence, **Option B** 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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More Questions from Mathematics of Finance

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Rs.1,25,000\displaystyle 1,25,000 is borrowed at compound interest at the rate of 2%\displaystyle 2\% for the 1st year, 3%\displaystyle 3\% for the second year and 4%\displaystyle 4\% for the 3rd year. Find the amount to be paid after 3 years.

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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