Mathematics for FinancePYQ Dec 22Question 1457 of 512
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A company establishes a sinking fund to provide for the payment ₹2,00,000\displaystyle ₹ 2,00,000 debt maturity in 20\displaystyle 20 years contribution to the fund are to be made at the end of every year. Find amount of each deposit if interest is 10%\displaystyle 10\% p.a.?

Options

A₹3,592.11\displaystyle ₹ 3,592.11
B₹3,492.11\displaystyle ₹ 3,492.11
C₹3,392.11\displaystyle ₹ 3,392.11
DNone of these
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Correct Answer

✅ Option b — ₹3,492.11\displaystyle ₹ 3,492.11

All Options:

  • A₹3,592.11\displaystyle ₹ 3,592.11
  • B₹3,492.11\displaystyle ₹ 3,492.11
  • C₹3,392.11\displaystyle ₹ 3,392.11
  • DNone of these

Detailed Solution & Explanation

Let the annual deposit in the sinking fund be A\displaystyle A. Given parameters: * Target Future Value (FV\displaystyle FV) = Rs. 2,00,000\displaystyle \text{Rs. }2,00,000 * Time (n\displaystyle n) = 20\displaystyle 20 years * Interest Rate (r\displaystyle r) = 10%\displaystyle 10\% p.a. compounded annually, so i=0.10\displaystyle i = 0.10 The formula for the Future Value of an ordinary annuity is: FV=A×(1+i)n−1iFV = A \times \frac{(1+i)^n - 1}{i} Substituting the values: 2,00,000=A×(1.10)20−10.102,00,000 = A \times \frac{(1.10)^{20} - 1}{0.10} First, let's calculate (1.10)20\displaystyle (1.10)^{20}: (1.10)20≈6.727500(1.10)^{20} \approx 6.727500 Now substitute this back: 2,00,000=A×6.727500−10.102,00,000 = A \times \frac{6.727500 - 1}{0.10} 2,00,000=57.275A2,00,000 = 57.275 A Solving for A\displaystyle A: A=2,00,00057.275≈3,492.11A = \frac{2,00,000}{57.275} \approx 3,492.11 Thus, the annual deposit is approximately Rs. 3,492.11\displaystyle \text{Rs. }3,492.11. Hence, **Option B** is the correct answer.

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