Mathematics of FinanceMCQPYQ Dec 23Question 1256 of 512
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The population of a city increases at the rate of 5%\displaystyle 5\% every year. What will be the population of the city in the year 2023\displaystyle 2023, if its population in 2021\displaystyle 2021 was 1,00,000\displaystyle 1,00,000?

Options

A1,05,000\displaystyle 1,05,000
B1,10,250\displaystyle 1,10,250
C1,15,240\displaystyle 1,15,240
D1,20,550\displaystyle 1,20,550
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Correct Answer

Option b1,10,250\displaystyle 1,10,250

All Options:

  • A1,05,000\displaystyle 1,05,000
  • B1,10,250\displaystyle 1,10,250
  • C1,15,240\displaystyle 1,15,240
  • D1,20,550\displaystyle 1,20,550

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Detailed Solution & Explanation

**Derivation of Population Growth** Given: - Population in 2021\displaystyle 2021 (P0\displaystyle P_0) = 1,00,000\displaystyle 1,00,000 - Growth rate (r\displaystyle r) = 5%\displaystyle 5\% per annum - Time (t\displaystyle t) = 2\displaystyle 2 years (from 2021\displaystyle 2021 to 2023\displaystyle 2023) **Step 1: Calculate the future population (P2\displaystyle P_2)** P2=P0(1+r)tP_2 = P_0(1 + r)^t P2=100000(1+0.05)2P_2 = 100000(1 + 0.05)^2 P2=100000(1.05)2P_2 = 100000(1.05)^2 P2=100000×1.1025=1,10,250P_2 = 100000 \times 1.1025 = 1,10,250 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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