Mathematics for FinanceMTP June 24 Series IQuestion 1411 of 512
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What will be the population after 3 years , when present population is 1,00,000\displaystyle 1,00,000 and the population increases at 3%\displaystyle 3\% in 1st year, at 4%\displaystyle 4\% in second year and at 5%\displaystyle 5\% in third year

Options

A1,12,476\displaystyle 1,12,476
B1,12,576\displaystyle 1,12,576
C1,20,576\displaystyle 1,20,576
D1,25,600\displaystyle 1,25,600
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Correct Answer

✅ Option a — 1,12,476\displaystyle 1,12,476

All Options:

  • A1,12,476\displaystyle 1,12,476
  • B1,12,576\displaystyle 1,12,576
  • C1,20,576\displaystyle 1,20,576
  • D1,25,600\displaystyle 1,25,600

Detailed Solution & Explanation

To find the population after 3\displaystyle 3 years, we apply the compound interest formula with successive growth rates: A=P(1+r1100)(1+r2100)(1+r3100)A = P \left(1 + \frac{r_1}{100}\right) \left(1 + \frac{r_2}{100}\right) \left(1 + \frac{r_3}{100}\right) Given parameters: * Present Population (P\displaystyle P) = 1,00,000\displaystyle 1,00,000 * Growth rate in the 1st year (r1\displaystyle r_1) = 3%\displaystyle 3\% * Growth rate in the 2nd year (r2\displaystyle r_2) = 4%\displaystyle 4\% * Growth rate in the 3rd year (r3\displaystyle r_3) = 5%\displaystyle 5\% Substituting the values: A=1,00,000×(1+3100)×(1+4100)×(1+5100)A = 1,00,000 \times \left(1 + \frac{3}{100}\right) \times \left(1 + \frac{4}{100}\right) \times \left(1 + \frac{5}{100}\right) A=1,00,000×1.03×1.04×1.05A = 1,00,000 \times 1.03 \times 1.04 \times 1.05 Let's calculate step-by-step: 1,00,000×1.03=1,03,0001,00,000 \times 1.03 = 1,03,000 1,03,000×1.04=1,07,1201,03,000 \times 1.04 = 1,07,120 1,07,120×1.05=1,12,4761,07,120 \times 1.05 = 1,12,476 Thus, the population after 3\displaystyle 3 years will be 1,12,476\displaystyle 1,12,476. Hence, **Option A** is the correct answer.

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