Mathematics of FinanceMCQPYQ July 21Question 1550 of 512
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If the nominal rate of growth is 17%\displaystyle 17\% and inflation is 9%\displaystyle 9\% for the five years. Let P be the Gross Domestic Product (GDP) amount at the present year then the projected real GDP after 6\displaystyle 6 years is:

Options

A1.58\displaystyle 1.58 P
B1.921\displaystyle 1.921 P
C1.403\displaystyle 1.403 P
D2.51\displaystyle 2.51 P
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Correct Answer

Option a1.58\displaystyle 1.58 P

All Options:

  • A1.58\displaystyle 1.58 P
  • B1.921\displaystyle 1.921 P
  • C1.403\displaystyle 1.403 P
  • D2.51\displaystyle 2.51 P

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Detailed Solution & Explanation

The projected real GDP after 6\displaystyle 6 years can be calculated by adjusting the nominal GDP growth for inflation. The real growth rate rreal\displaystyle r_{\text{real}} is: 1+rreal=1+nominal growth rate1+inflation rate=1+0.171+0.09=1.171.091.0733941 + r_{\text{real}} = \frac{1 + \text{nominal growth rate}}{1 + \text{inflation rate}} = \frac{1 + 0.17}{1 + 0.09} = \frac{1.17}{1.09} \approx 1.073394 rreal7.3394%r_{\text{real}} \approx 7.3394\% The projected real GDP after 6\displaystyle 6 years is: GDP6=P(1+rreal)6=P(1.073394)61.528P\text{GDP}_6 = P (1 + r_{\text{real}})^6 = P (1.073394)^6 \approx 1.528 P Alternatively, using simple subtraction for the real growth rate (17%9%=8%\displaystyle 17\% - 9\% = 8\%): GDP6=P(1+0.08)6=P(1.08)61.587P\text{GDP}_6 = P (1 + 0.08)^6 = P (1.08)^6 \approx 1.587 P This matches Option A. 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.

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