Mathematics of FinanceMCQMTP Sep 24 - IQuestion 1588 of 512
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A stock pays annually an amount of Rs. 10\displaystyle 10 from 6th\displaystyle 6^{th} year onwards. What is the present value of perpetuity, if the rate of return is 20%\displaystyle 20\%.

Options

A20.1\displaystyle 20.1
B19.1\displaystyle 19.1
C21.1\displaystyle 21.1
D22.1\displaystyle 22.1
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Correct Answer

Option a20.1\displaystyle 20.1

All Options:

  • A20.1\displaystyle 20.1
  • B19.1\displaystyle 19.1
  • C21.1\displaystyle 21.1
  • D22.1\displaystyle 22.1

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Detailed Solution & Explanation

This is a deferred perpetuity where payments of A=10\displaystyle A = 10 start from Year 6\displaystyle 6 onwards. The value of the perpetuity at Year 5\displaystyle 5 is: V5=Ai=100.20=50V_5 = \frac{A}{i} = \frac{10}{0.20} = 50 Discounting V5\displaystyle V_5 back to the present (Year 0): PV=V5(1+i)5=50(1.20)520.1PV = \frac{V_5}{(1+i)^5} = \frac{50}{(1.20)^5} \approx 20.1 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.

View Official ICAI Syllabus

Exam Strategy Tip

Guaranteed 12-16 marks. Master your calculator! Learn the 'GT' and compound interest M+/M- tricks to solve annuity questions in 10 seconds without writing long formulas.

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