Mathematics of FinancePYQ Jan 26Question 4509 of 507
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A sinking fund is created for replacement of machine at the end of 20 years. Its present cost is ₹ 8,00,000. After 20 years cost of new machine would be ₹ 10,00,000, How much provision need to be made out of the profit each year provided sinking fund investments can earn interest at the rate of 7% pa? The scrap value of the machine at the end of 20 years would be ₹ 2,00,000. Given 1.0720=3.8697\displaystyle 1.07^{20}= 3.8697.

Options

A₹ 15,514
B₹ 13,514
C₹ 19,514
D₹ 17,514
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Correct Answer

Option c₹ 19,514

All Options:

  • A₹ 15,514
  • B₹ 13,514
  • C₹ 19,514
  • D₹ 17,514

Detailed Solution & Explanation

A sinking fund is created to accumulate the required sum of money for replacing the machine at the end of 20\displaystyle 20 years.

The net amount required to be accumulated is:
Required Amount (FV)=Cost of new machineScrap value of old machine\text{Required Amount } (FV) = \text{Cost of new machine} - \text{Scrap value of old machine}
FV=10,00,0002,00,000=₹ 8,00,000FV = 10,00,000 - 2,00,000 = \text{₹ } 8,00,000

The annual provision A\displaystyle A made at the end of each year is calculated using the future value of an ordinary annuity formula:
FV=A×[(1+i)n1i]FV = A \times \left[ \frac{(1 + i)^n - 1}{i} \right]
where:
- i=7%=0.07\displaystyle i = 7\% = 0.07 is the annual interest rate.
- n=20\displaystyle n = 20 years is the duration.
- Given: 1.0720=3.8697\displaystyle 1.07^{20} = 3.8697.

Substitute the values into the formula:
8,00,000=A×[1.072010.07]8,00,000 = A \times \left[ \frac{1.07^{20} - 1}{0.07} \right]
8,00,000=A×[3.869710.07]8,00,000 = A \times \left[ \frac{3.8697 - 1}{0.07} \right]
8,00,000=A×[2.86970.07]8,00,000 = A \times \left[ \frac{2.8697}{0.07} \right]
8,00,000=A×40.9957148,00,000 = A \times 40.995714
A=8,00,00040.99571419,514.28A = \frac{8,00,000}{40.995714} \approx 19,514.28
Thus, the annual provision required to be made is approximately ₹ 19,514.

Hence, **Option C** 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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