Mathematics of FinanceMCQMTP 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 aRs.5600\displaystyle 5600

All Options:

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

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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) = 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=2800.140.09=2800.05=5,600PV = \frac{280}{0.14 - 0.09} = \frac{280}{0.05} = 5,600 Hence, **Option A** 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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