Mathematics of FinanceMCQMTP June 24 Series IIIQuestion 1540 of 512
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A sinking fund is created for redeeming debentures worth Rs. 5,00,000\displaystyle 5,00,000 at the end of 25\displaystyle 25 years. How much provision need to be made out of profits each year provided sinking fund investments can earn at 4%\displaystyle 4\% per annum

Options

A12,006\displaystyle 12,006
B12,040\displaystyle 12,040
C12039\displaystyle 12039
D12035\displaystyle 12035
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Correct Answer

Option a12,006\displaystyle 12,006

All Options:

  • A12,006\displaystyle 12,006
  • B12,040\displaystyle 12,040
  • C12039\displaystyle 12039
  • D12035\displaystyle 12035

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Detailed Solution & Explanation

The annual provision (A\displaystyle A) required 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) = 5,00,000\displaystyle 5,00,000 * Time (n\displaystyle n) = 25\displaystyle 25 years * Interest rate (i\displaystyle i) = 4%\displaystyle 4\% p.a. = 0.04\displaystyle 0.04 Substituting the values: A=5,00,000[(1.04)2510.04]A = \frac{5,00,000}{\left[ \frac{(1.04)^{25} - 1}{0.04} \right]} Using (1.04)252.665836\displaystyle (1.04)^{25} \approx 2.665836: A=5,00,00041.645912,005.9812,006A = \frac{5,00,000}{41.6459} \approx 12,005.98 \approx 12,006 Hence, **Option A** 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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