Mathematics for FinancePYQ 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

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.

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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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