Mathematics for FinanceMTP Sep 24 - IQuestion 1588 of 512
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A stock pays annually an amount of Rs. 10\displaystyle 10 from 6th\displaystyle 6^{th} year onwards. What is the present value of perpetuity, if the rate of return is 20%\displaystyle 20\%.

Options

A20.1\displaystyle 20.1
B19.1\displaystyle 19.1
C21.1\displaystyle 21.1
D22.1\displaystyle 22.1
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Correct Answer

✅ Option a — 20.1\displaystyle 20.1

All Options:

  • A20.1\displaystyle 20.1
  • B19.1\displaystyle 19.1
  • C21.1\displaystyle 21.1
  • D22.1\displaystyle 22.1

Detailed Solution & Explanation

This is a deferred perpetuity where payments of A=10\displaystyle A = 10 start from Year 6\displaystyle 6 onwards. The value of the perpetuity at Year 5\displaystyle 5 is: V5=Ai=100.20=50V_5 = \frac{A}{i} = \frac{10}{0.20} = 50 Discounting V5\displaystyle V_5 back to the present (Year 0): PV=V5(1+i)5=50(1.20)5≈20.1PV = \frac{V_5}{(1+i)^5} = \frac{50}{(1.20)^5} \approx 20.1 Hence, **Option A** is the correct answer.

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