Mathematics of FinanceMCQMTP 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 a35\displaystyle 35 years

All Options:

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

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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=39.419.4=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)0.6931470.01980335 yearst = \frac{\ln(2)}{\ln(1.02)} \approx \frac{0.693147}{0.019803} \approx 35 \text{ years} 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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