Mathematics of FinanceMCQMTP June 24 Series IQuestion 1411 of 512
All Questions

What will be the population after 3 years , when present population is 1,00,000\displaystyle 1,00,000 and the population increases at 3%\displaystyle 3\% in 1st year, at 4%\displaystyle 4\% in second year and at 5%\displaystyle 5\% in third year

Options

A1,12,476\displaystyle 1,12,476
B1,12,576\displaystyle 1,12,576
C1,20,576\displaystyle 1,20,576
D1,25,600\displaystyle 1,25,600
For any discrepancies in this question, email contact@cadada.in

Correct Answer

Option a1,12,476\displaystyle 1,12,476

All Options:

  • A1,12,476\displaystyle 1,12,476
  • B1,12,576\displaystyle 1,12,576
  • C1,20,576\displaystyle 1,20,576
  • D1,25,600\displaystyle 1,25,600

Ad

Detailed Solution & Explanation

To find the population after 3\displaystyle 3 years, we apply the compound interest formula with successive growth rates: A=P(1+r1100)(1+r2100)(1+r3100)A = P \left(1 + \frac{r_1}{100}\right) \left(1 + \frac{r_2}{100}\right) \left(1 + \frac{r_3}{100}\right) Given parameters: * Present Population (P\displaystyle P) = 1,00,000\displaystyle 1,00,000 * Growth rate in the 1st year (r1\displaystyle r_1) = 3%\displaystyle 3\% * Growth rate in the 2nd year (r2\displaystyle r_2) = 4%\displaystyle 4\% * Growth rate in the 3rd year (r3\displaystyle r_3) = 5%\displaystyle 5\% Substituting the values: A=1,00,000×(1+3100)×(1+4100)×(1+5100)A = 1,00,000 \times \left(1 + \frac{3}{100}\right) \times \left(1 + \frac{4}{100}\right) \times \left(1 + \frac{5}{100}\right) A=1,00,000×1.03×1.04×1.05A = 1,00,000 \times 1.03 \times 1.04 \times 1.05 Let's calculate step-by-step: 1,00,000×1.03=1,03,0001,00,000 \times 1.03 = 1,03,000 1,03,000×1.04=1,07,1201,03,000 \times 1.04 = 1,07,120 1,07,120×1.05=1,12,4761,07,120 \times 1.05 = 1,12,476 Thus, the population after 3\displaystyle 3 years will be 1,12,476\displaystyle 1,12,476. 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