Mathematics for FinanceMTP Nov 21Question 1333 of 512
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What will be population after 3\displaystyle 3 years when present population is 25,000\displaystyle 25,000 and population increases at the rate of 3%\displaystyle 3\% in 1\displaystyle 1 year, at 4%\displaystyle 4\% in II\displaystyle II year and 5%\displaystyle 5\% in III\displaystyle III year?

Options

ARs.28,119\displaystyle 28,119
BRs.29,118\displaystyle 29,118
CRs.27,000\displaystyle 27,000
DRs.30,000\displaystyle 30,000
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Correct Answer

✅ Option a — Rs.28,119\displaystyle 28,119

All Options:

  • ARs.28,119\displaystyle 28,119
  • BRs.29,118\displaystyle 29,118
  • CRs.27,000\displaystyle 27,000
  • DRs.30,000\displaystyle 30,000

Detailed Solution & Explanation

**Derivation of Population Growth with Varying Rates** Given: - Present Population (P0\displaystyle P_0) = 25,000\displaystyle 25,000 - Growth rates: r1=3%\displaystyle r_1 = 3\%, r2=4%\displaystyle r_2 = 4\%, r3=5%\displaystyle r_3 = 5\% **Step 1: Set up the growth equation** P3=P0(1+r1)(1+r2)(1+r3)P_3 = P_0(1 + r_1)(1 + r_2)(1 + r_3) P3=25000(1+0.03)(1+0.04)(1+0.05)P_3 = 25000(1 + 0.03)(1 + 0.04)(1 + 0.05) P3=25000(1.03)(1.04)(1.05)P_3 = 25000(1.03)(1.04)(1.05) **Step 2: Calculate the product** 1.03×1.04×1.05=1.124761.03 \times 1.04 \times 1.05 = 1.12476 P3=25000×1.12476=28,119P_3 = 25000 \times 1.12476 = 28,119 Hence, **Option A** is the correct answer.

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