Mathematics for FinanceMTP Jun 23 - Series IIQuestion 1590 of 512
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If discounted rate is 14%\displaystyle 14\% per annum, then how much company has to receive Rs.280\displaystyle 280 growing at 9%\displaystyle 9\% annually forever?

Options

ARs.5600\displaystyle 5600
BRs.2800\displaystyle 2800
CRs.1400\displaystyle 1400
DRs.4200\displaystyle 4200
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Correct Answer

✅ Option a — Rs.5600\displaystyle 5600

All Options:

  • ARs.5600\displaystyle 5600
  • BRs.2800\displaystyle 2800
  • CRs.1400\displaystyle 1400
  • DRs.4200\displaystyle 4200

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) = 280\displaystyle 280 * Discount rate (r\displaystyle r) = 14%\displaystyle 14\% p.a. = 0.14\displaystyle 0.14 * Growth rate (g\displaystyle g) = 9%\displaystyle 9\% p.a. = 0.09\displaystyle 0.09 Substituting the values: PV=2800.14−0.09=2800.05=5,600PV = \frac{280}{0.14 - 0.09} = \frac{280}{0.05} = 5,600 Hence, **Option A** is the correct answer.

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