Mathematics of FinanceMCQPYQ Sep 24Question 1564 of 512
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A Perpetuity has a cash flow of $625$ and a required rate of return of $8\%$. If the cash flow is expected to grow at a constant rate of $4\%$ per year, then the intrinsic value of this perpetuity (present value of growing perpetuity) is:

Select Your Answer (Keyboard: A, B, C, D)
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Correct Answer

✅ Option b — $15,625$

All Options:

  • A$15,000$
  • B$15,625$
  • C$14,280$
  • D$16,667$

Detailed Solution & Explanation

The present value (PV\displaystyle PV) of a growing perpetuity is: PV=Ar−gPV = Ar−g\displaystyle \frac{A}{r - g} Given: * Cash flow (A\displaystyle A) = $625$ * Required rate of return (r\displaystyle r) = 8%\displaystyle 8\% p.a. = $0.08$ * Growth rate (g\displaystyle g) = 4%\displaystyle 4\% p.a. = $0.04$ Substituting the values: PV=6250.08−0.04=6250.04=15,625PV = \displaystyle \frac{625}{0.08 - 0.04} = \frac{625}{0.04} = 15,625 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

Exam Strategy Tip

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