Mathematics of FinanceMCQMTP Dec 22 - Series IQuestion 1581 of 512
All Questions

Determine the present value of perpetuity of 50,000\displaystyle 50,000 per month at the rate interest 12%\displaystyle 12\% p.a.

Options

A45,00,000\displaystyle 45,00,000
B50,00,000\displaystyle 50,00,000
C55,00,000\displaystyle 55,00,000
D60,00,000\displaystyle 60,00,000
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Correct Answer

Option c55,00,000\displaystyle 55,00,000

All Options:

  • A45,00,000\displaystyle 45,00,000
  • B50,00,000\displaystyle 50,00,000
  • C55,00,000\displaystyle 55,00,000
  • D60,00,000\displaystyle 60,00,000

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Detailed Solution & Explanation

The present value of a perpetuity is: PV=AiPV = \frac{A}{i} Given: * Monthly payment (A\displaystyle A) = 50,000\displaystyle 50,000 * Nominal rate = 12%\displaystyle 12\% p.a., so periodic monthly rate i=12%12=1%=0.01\displaystyle i = \frac{12\%}{12} = 1\% = 0.01 Substituting the values: PV=50,0000.01=50,00,000PV = \frac{50,000}{0.01} = 50,00,000 Mathematically, the present value is 50,00,000\displaystyle 50,00,000 (Option B). However, the official key marks Option C (55,00,000\displaystyle 55,00,000). 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

Exam Strategy Tip

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