Mathematics for FinanceMTP Nov 20Question 1312 of 512
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What will be the population after three years when present population is 25,000\displaystyle 25,000 and population increases at the rate 3%\displaystyle 3\% in first year, 4%\displaystyle 4\% in second year and 5%\displaystyle 5\% in third year?

Options

A28119\displaystyle 28119
B29118\displaystyle 29118
C27000\displaystyle 27000
D30000\displaystyle 30000
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Correct Answer

✅ Option a — 28119\displaystyle 28119

All Options:

  • A28119\displaystyle 28119
  • B29118\displaystyle 29118
  • C27000\displaystyle 27000
  • D30000\displaystyle 30000

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\% (1st year), r2=4%\displaystyle r_2 = 4\% (2nd year), r3=5%\displaystyle r_3 = 5\% (3rd year) **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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