Mathematics for FinancePYQ 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 b — 2,50,000\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

Detailed Solution & Explanation

The present value (PV\displaystyle PV) of a growing perpetuity is: PV=Ar−gPV = \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=2,5000.10−0.08=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.

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