Mathematics for FinanceMTP Apr 21Question 1323 of 512
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The annual birth and death rates per 1000\displaystyle 1000 are 39.4\displaystyle 39.4 and 19.4\displaystyle 19.4 respectively. The number of years in which the population will 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
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Correct Answer

✅ Option a — 35\displaystyle 35 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} Hence, **Option A** is the correct answer.

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