Mathematics for FinanceMTP Mar 22/ RTP Sep 24Question 1350 of 512
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What will be the population after 3\displaystyle 3 years when present population is 25000\displaystyle 25000, if the population increases at the rate 3%\displaystyle 3\% in I year, 4%\displaystyle 4\% in II year and 5%\displaystyle 5\% in III year.

Options

A28,119\displaystyle 28,119
B29,118\displaystyle 29,118
C27,000\displaystyle 27,000
D30,000\displaystyle 30,000
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Correct Answer

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

All Options:

  • A28,119\displaystyle 28,119
  • B29,118\displaystyle 29,118
  • C27,000\displaystyle 27,000
  • D30,000\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 *(Note: The database lists Option D (30,000\displaystyle 30,000) as correct, which is a typo in the key. The mathematically correct result is 28,119, which is Option A.)* Hence, **Option A** is the correct answer.

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