Mathematics for FinanceMTP Dec 23 Series IQuestion 1394 of 512
All Questions

The annual birth and death rates per 1,000\displaystyle 1,000 are 39.4\displaystyle 39.4 and 19.4\displaystyle 19.4 respectively. The number of years in which the population will be doubled assuming there is no immigration or emigration is

Options

A35\displaystyle 35 years
B30\displaystyle 30 years
C25\displaystyle 25 years
DNone of these
For any discrepancies in this question, email contact@cadada.in

Correct Answer

✅ Option c — 25\displaystyle 25 years

All Options:

  • A35\displaystyle 35 years
  • B30\displaystyle 30 years
  • C25\displaystyle 25 years
  • DNone of these

Detailed Solution & Explanation

**Derivation of Population Doubling Time** Given: - Birth rate = 39.4\displaystyle 39.4 per 1,000\displaystyle 1,000 - Death rate = 19.4\displaystyle 19.4 per 1,000\displaystyle 1,000 **Step 1: Calculate the net annual growth rate (r\displaystyle r)** Net Growth Rate per 1,000=39.4−19.4=20\text{Net Growth Rate per 1,000} = 39.4 - 19.4 = 20 r=201000=2%=0.02 per annumr = \frac{20}{1000} = 2\% = 0.02 \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 = \frac{\ln(2)}{\ln(1.02)} \approx \frac{0.693147}{0.019803} \approx 35 \text{ years} *(Note: The database lists Option C (25\displaystyle 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.

More Questions from Mathematics for Finance

Ready to Master Mathematics for Finance?

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

Start Practicing — It's Free