Mathematics of FinanceMCQMTP Mar 22/ RTP Sep 24Question 1350 of 512
All Questions

What will be the population after 3\displaystyle 3 years when present population is 25000\displaystyle 25000, if the population increases at the rate 3%\displaystyle 3\% in I year, 4%\displaystyle 4\% in II year and 5%\displaystyle 5\% in III year.

Options

A28,119\displaystyle 28,119
B29,118\displaystyle 29,118
C27,000\displaystyle 27,000
D30,000\displaystyle 30,000
For any discrepancies in this question, email contact@cadada.in

Correct Answer

Option a28,119\displaystyle 28,119

All Options:

  • A28,119\displaystyle 28,119
  • B29,118\displaystyle 29,118
  • C27,000\displaystyle 27,000
  • D30,000\displaystyle 30,000

Ad

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 *(Note: The database lists Option D (30,000\displaystyle 30,000) as correct, which is a typo in the key. The mathematically correct result is 28,119, which is 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.

View Official ICAI Syllabus

Exam Strategy Tip

Guaranteed 12-16 marks. Master your calculator! Learn the 'GT' and compound interest M+/M- tricks to solve annuity questions in 10 seconds without writing long formulas.

Related Comparison Tables

More Questions from Mathematics of Finance

Ready to Master Mathematics of Finance?

Practice all 512 questions with instant feedback, earn XP, track your streaks, and ace your CA Foundation exam.

Start Practicing — It's Free