Mathematics of FinanceMCQPYQ June 22Question 1554 of 512
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Assuming that the discount rate is 7%\displaystyle 7\% p.a. How much would you pay to receive 200\displaystyle 200, growing at 5%\displaystyle 5\% annually forever?

Options

A2,500\displaystyle 2,500
B5,000\displaystyle 5,000
C7,500\displaystyle 7,500
D10,000\displaystyle 10,000
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Correct Answer

Option d10,000\displaystyle 10,000

All Options:

  • A2,500\displaystyle 2,500
  • B5,000\displaystyle 5,000
  • C7,500\displaystyle 7,500
  • D10,000\displaystyle 10,000

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Detailed Solution & Explanation

The present value (PV\displaystyle PV) of a growing perpetuity is: PV=ArgPV = \frac{A}{r - g} Given: * First cash flow (A\displaystyle A) = 200\displaystyle 200 * Discount rate (r\displaystyle r) = 7%\displaystyle 7\% p.a. = 0.07\displaystyle 0.07 * Growth rate (g\displaystyle g) = 5%\displaystyle 5\% p.a. = 0.05\displaystyle 0.05 Substituting the values: PV=2000.070.05=2000.02=10,000PV = \frac{200}{0.07 - 0.05} = \frac{200}{0.02} = 10,000 This matches Option D (10,000\displaystyle 10,000). Hence, **Option D** 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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