Mathematics of FinanceMCQMTP Nov 20Question 1312 of 512
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What will be the population after three years when present population is 25,000\displaystyle 25,000 and population increases at the rate 3%\displaystyle 3\% in first year, 4%\displaystyle 4\% in second year and 5%\displaystyle 5\% in third year?

Options

A28119\displaystyle 28119
B29118\displaystyle 29118
C27000\displaystyle 27000
D30000\displaystyle 30000
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Correct Answer

Option a28119\displaystyle 28119

All Options:

  • A28119\displaystyle 28119
  • B29118\displaystyle 29118
  • C27000\displaystyle 27000
  • D30000\displaystyle 30000

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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\% (1st year), r2=4%\displaystyle r_2 = 4\% (2nd year), r3=5%\displaystyle r_3 = 5\% (3rd year) **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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