Mathematics of FinanceMCQMTP Dec 23 Series IQuestion 1394 of 512
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The annual birth and death rates per $1,000\displaystyle are $39.4 and $19.4$ respectively. The number of years in which the population will be doubled assuming there is no immigration or emigration is

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

✅ Option c — $25$ years

All Options:

  • A$35$ years
  • B$30$ years
  • C$25$ years
  • DNone of these

Detailed Solution & Explanation

**Derivation of Population Doubling Time** Given: - Birth rate = $39.4\displaystyle per $1,000 - Death rate = $19.4\displaystyle per $1,000 **Step 1: Calculate the net annual growth rate (r\displaystyle r)** Net Growth Rate per 1,000=39.4−19.4=20Net Growth Rate per 1,000=39\displaystyle \text{Net Growth Rate per 1,000} = 39.4 - 19.4 = 20 r=201000=2%=0.02 per annumr = 201000=2\displaystyle \frac{20}{1000} = 2\% = 0.02  per annum\displaystyle \text{ per annum} **Step 2: Set up the population doubling equation** (1+r)t=2(1 + r)^t = 2 (1.02)t=2(1.02)^t = 2 **Step 3: Solve for t\displaystyle t using logarithms** t=ln⁡(2)ln⁡(1.02)≈0.6931470.019803≈35 yearst = ln⁡(2)ln⁡(1.02)\displaystyle \frac{\ln(2)}{\ln(1.02)} ≈\displaystyle \approx 0.6931470.019803\displaystyle \frac{0.693147}{0.019803} ≈\displaystyle \approx 35  years\displaystyle \text{ years} *(Note: The database lists Option C ($25$ years) as correct, which is mathematically incorrect. The correct period is 35 years, 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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