Mathematics of FinanceMCQPYQ July 21Question 1549 of 512
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If discount rate is 14%\displaystyle 14\% per annum, then how much a company has to pay to receive 280\displaystyle 280 growing at 9%\displaystyle 9\% annually forever?

Options

A5,600\displaystyle 5,600
B2,800\displaystyle 2,800
C1,400\displaystyle 1,400
D4,200\displaystyle 4,200
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Correct Answer

Option b2,800\displaystyle 2,800

All Options:

  • A5,600\displaystyle 5,600
  • B2,800\displaystyle 2,800
  • C1,400\displaystyle 1,400
  • D4,200\displaystyle 4,200

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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 Mathematically, the value is 5,600\displaystyle 5,600 (Option A). However, the official key marks Option B (2,800\displaystyle 2,800). 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

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