Mathematics of FinanceMCQMTP Nov 21Question 1333 of 512
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What will be population after 3\displaystyle 3 years when present population is 25,000\displaystyle 25,000 and population increases at the rate of 3%\displaystyle 3\% in 1\displaystyle 1 year, at 4%\displaystyle 4\% in II\displaystyle II year and 5%\displaystyle 5\% in III\displaystyle III year?

Options

ARs.28,119\displaystyle 28,119
BRs.29,118\displaystyle 29,118
CRs.27,000\displaystyle 27,000
DRs.30,000\displaystyle 30,000
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Correct Answer

Option aRs.28,119\displaystyle 28,119

All Options:

  • ARs.28,119\displaystyle 28,119
  • BRs.29,118\displaystyle 29,118
  • CRs.27,000\displaystyle 27,000
  • DRs.30,000\displaystyle 30,000

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Detailed Solution & Explanation

**Derivation of Population Growth with Varying Rates** Given: - Present Population (P0\displaystyle P_0) = 25,000\displaystyle 25,000 - Growth rates: r1=3%\displaystyle r_1 = 3\%, r2=4%\displaystyle r_2 = 4\%, r3=5%\displaystyle r_3 = 5\% **Step 1: Set up the growth equation** P3=P0(1+r1)(1+r2)(1+r3)P_3 = P_0(1 + r_1)(1 + r_2)(1 + r_3) P3=25000(1+0.03)(1+0.04)(1+0.05)P_3 = 25000(1 + 0.03)(1 + 0.04)(1 + 0.05) P3=25000(1.03)(1.04)(1.05)P_3 = 25000(1.03)(1.04)(1.05) **Step 2: Calculate the product** 1.03×1.04×1.05=1.124761.03 \times 1.04 \times 1.05 = 1.12476 P3=25000×1.12476=28,119P_3 = 25000 \times 1.12476 = 28,119 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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