Mathematics of FinanceMCQPYQ Nov 19Question 1372 of 512
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What will be the population after 3\displaystyle 3 years when present population is Rs. 25,000\displaystyle \text{Rs. }25,000 and population increases at the rate of 3%\displaystyle 3\% in 1st\displaystyle 1^{st} year, at 4%\displaystyle 4\% in 2nd\displaystyle 2^{nd} year and 5%\displaystyle 5\% in 3rd\displaystyle 3^{rd} year?

Options

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

Option aRs. 28,119\displaystyle \text{Rs. }28,119

All Options:

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

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Detailed Solution & Explanation

**Derivation of Population after 3 Years** Given: - Present Population (P0\displaystyle P_0) = 25,000\displaystyle 25,000 - Growth rate in year 1 (r1\displaystyle r_1) = 3%\displaystyle 3\% - Growth rate in year 2 (r2\displaystyle r_2) = 4%\displaystyle 4\% - Growth rate in year 3 (r3\displaystyle r_3) = 5%\displaystyle 5\% **Step 1: Set up the compound growth formula for successive rates** P3=P0(1+r1)(1+r2)(1+r3)P_3 = P_0(1 + r_1)(1 + r_2)(1 + r_3) P3=25000(1+3100)(1+4100)(1+5100)P_3 = 25000\left(1 + \frac{3}{100}\right)\left(1 + \frac{4}{100}\right)\left(1 + \frac{5}{100}\right) **Step 2: Calculate the population** P3=25000×1.03×1.04×1.05P_3 = 25000 \times 1.03 \times 1.04 \times 1.05 P3=25750×1.04×1.05P_3 = 25750 \times 1.04 \times 1.05 P3=26780×1.05=28,119P_3 = 26780 \times 1.05 = 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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