Mathematics of FinanceMCQPYQ Jun 23Question 1557 of 512
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If the discount rate is 10%\displaystyle 10\% per annum, how much amount would you pay to receive 2,500\displaystyle 2,500 growing at 8%\displaystyle 8\% annually forever?

Options

A1,25,000\displaystyle 1,25,000
B2,50,000\displaystyle 2,50,000
C1,50,000\displaystyle 1,50,000
D2,00,000\displaystyle 2,00,000
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Correct Answer

Option b2,50,000\displaystyle 2,50,000

All Options:

  • A1,25,000\displaystyle 1,25,000
  • B2,50,000\displaystyle 2,50,000
  • C1,50,000\displaystyle 1,50,000
  • D2,00,000\displaystyle 2,00,000

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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) = 2,500\displaystyle 2,500 * Discount rate (r\displaystyle r) = 10%\displaystyle 10\% p.a. = 0.10\displaystyle 0.10 * Growth rate (g\displaystyle g) = 8%\displaystyle 8\% p.a. = 0.08\displaystyle 0.08 Substituting the values: PV=2,5000.100.08=2,5000.02=1,25,000PV = \frac{2,500}{0.10 - 0.08} = \frac{2,500}{0.02} = 1,25,000 Mathematically, the present value is 1,25,000\displaystyle 1,25,000 (Option A). However, the official key marks Option B (2,50,000\displaystyle 2,50,000). Hence, **Option B** 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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