Mathematics of FinanceMCQPYQ Nov. 20Question 1546 of 512
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Determine the present value of perpetuity of 50,000\displaystyle 50,000 per month @ rate of interest 12%\displaystyle 12\% p.a. is

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