Mathematics of FinanceMCQMTP Sep 24 Series IIQuestion 1543 of 512
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A company establishes a sinking fund to provide for the payment of 2,00,000\displaystyle 2,00,000 debt maturing in 20\displaystyle 20 years. Contributions to the fund are to be made at the end of every year. Find the amount of each annual deposit if interest is 8%\displaystyle 8\% per annum

Options

A6,142\displaystyle 6,142
B6,049\displaystyle 6,049
C6,052\displaystyle 6,052
D6,159\displaystyle 6,159
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Correct Answer

Option b6,049\displaystyle 6,049

All Options:

  • A6,142\displaystyle 6,142
  • B6,049\displaystyle 6,049
  • C6,052\displaystyle 6,052
  • D6,159\displaystyle 6,159

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Detailed Solution & Explanation

The annual contribution (A\displaystyle A) for the sinking fund is: A=FV[(1+i)n1i]A = \frac{FV}{\left[ \frac{(1+i)^n - 1}{i} \right]} Given: * Future Value (FV\displaystyle FV) = 2,00,000\displaystyle 2,00,000 * Time (n\displaystyle n) = 20\displaystyle 20 years * Interest rate (i\displaystyle i) = 8%\displaystyle 8\% p.a. = 0.08\displaystyle 0.08 Substituting the values: Annuity factor=(1.08)2010.084.66095710.08=45.76196\text{Annuity factor} = \frac{(1.08)^{20} - 1}{0.08} \approx \frac{4.660957 - 1}{0.08} = 45.76196 A=2,00,00045.761964,370.44A = \frac{2,00,000}{45.76196} \approx 4,370.44 Mathematically, the contribution is 4,370.44\displaystyle 4,370.44. However, the official key marks Option B (6,049\displaystyle 6,049). 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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