Mathematics of FinanceMCQMTP June 22Question 1354 of 512
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The present population of a town is $25,000$. If it grows at the rate of $4\%,\displaystyle ,5\%,\displaystyle ,8\%during\displaystyle during1^{st}year,\displaystyle year,2^{nd}year,\displaystyle year,3^{rd}$ year respectively. Then find the population after $3$ years.

Select Your Answer (Keyboard: A, B, C, D)
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Correct Answer

✅ Option a — $29,484$

All Options:

  • A$29,484$
  • B$29,844$
  • C$28,448$
  • D$28,944$

Detailed Solution & Explanation

**Derivation of Population Growth with Varying Rates** Given: - Present Population (P0\displaystyle P_0) = $25,000$ - Growth rates: r1=4%\displaystyle r_1 = 4\%, r2=5%\displaystyle r_2 = 5\%, r3=8%\displaystyle r_3 = 8\% **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+0.04)(1+0.05)(1+0.08)P_3 = 25000(1 + 0.04)(1 + 0.05)(1 + 0.08) P3=25000(1.04)(1.05)(1.08)P_3 = 25000(1.04)(1.05)(1.08) **Step 2: Calculate the product** 1.04×1.05×1.08=1.179361.04 ×\displaystyle \times 1.05 ×\displaystyle \times 1.08 = 1.17936 P3=25000×1.17936=29,484P_3 = 25000 ×\displaystyle \times 1.17936 = 29,484 *(Note: The database lists Option C ($28,448$) as correct, which is a transposition error in the digits of 29,484. The mathematically correct population is 29,484, 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

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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.

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