Mathematics of FinanceMCQPYQ 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

A3,592.11\displaystyle ₹ 3,592.11
B3,492.11\displaystyle ₹ 3,492.11
C3,392.11\displaystyle ₹ 3,392.11
DNone of these
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Correct Answer

Option b3,492.11\displaystyle ₹ 3,492.11

All Options:

  • A3,592.11\displaystyle ₹ 3,592.11
  • B3,492.11\displaystyle ₹ 3,492.11
  • C3,392.11\displaystyle ₹ 3,392.11
  • DNone of these

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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)n1iFV = A \times \frac{(1+i)^n - 1}{i} Substituting the values: 2,00,000=A×(1.10)2010.102,00,000 = A \times \frac{(1.10)^{20} - 1}{0.10} First, let's calculate (1.10)20\displaystyle (1.10)^{20}: (1.10)206.727500(1.10)^{20} \approx 6.727500 Now substitute this back: 2,00,000=A×6.72750010.102,00,000 = A \times \frac{6.727500 - 1}{0.10} 2,00,000=57.275A2,00,000 = 57.275 A Solving for A\displaystyle A: A=2,00,00057.2753,492.11A = \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.

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.

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