Mathematics of FinanceMCQPYQ Dec 23Question 1558 of 512
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Mr. Sharad got his retirement benefits amounting to 50,00,000\displaystyle 50,00,000. He want to receive a fixed monthly sum of amount for his rest of life, starting after one month and thereafter he want to pass on the same to future generation. He expects to earn an interest of 9%\displaystyle 9\% CI Annually. Determine how much perpetual payment he will receive every month?

Options

A39,500\displaystyle 39,500
B38,500\displaystyle 38,500
C37,500\displaystyle 37,500
D36,600\displaystyle 36,600
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Correct Answer

Option c37,500\displaystyle 37,500

All Options:

  • A39,500\displaystyle 39,500
  • B38,500\displaystyle 38,500
  • C37,500\displaystyle 37,500
  • D36,600\displaystyle 36,600

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Detailed Solution & Explanation

The present value of a perpetuity is: PV=AiPV = \frac{A}{i} Given: * Retirement benefit (PV\displaystyle PV) = 50,00,000\displaystyle 50,00,000 * Nominal annual rate = 9%\displaystyle 9\% p.a., so periodic monthly rate i=9%12=0.75%=0.0075\displaystyle i = \frac{9\%}{12} = 0.75\% = 0.0075 Substituting the values to find the monthly payment A\displaystyle A: 50,00,000=A0.007550,00,000 = \frac{A}{0.0075} A=50,00,000×0.0075=37,500A = 50,00,000 \times 0.0075 = 37,500 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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