Mathematics for FinanceMTP June 22Question 1354 of 512
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The present population of a town is 25,000\displaystyle 25,000. If it grows at the rate of 4%\displaystyle 4\%, 5%\displaystyle 5\%, 8%\displaystyle 8\% during 1st\displaystyle 1^{st} year, 2nd\displaystyle 2^{nd} year, 3rd\displaystyle 3^{rd} year respectively. Then find the population after 3\displaystyle 3 years.

Options

A29,484\displaystyle 29,484
B29,844\displaystyle 29,844
C28,448\displaystyle 28,448
D28,944\displaystyle 28,944
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Correct Answer

✅ Option a — 29,484\displaystyle 29,484

All Options:

  • A29,484\displaystyle 29,484
  • B29,844\displaystyle 29,844
  • C28,448\displaystyle 28,448
  • D28,944\displaystyle 28,944

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=4%\displaystyle r_1 = 4\%, r2=5%\displaystyle r_2 = 5\%, r3=8%\displaystyle r_3 = 8\% **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+0.04)(1+0.05)(1+0.08)P_3 = 25000(1 + 0.04)(1 + 0.05)(1 + 0.08) P3=25000(1.04)(1.05)(1.08)P_3 = 25000(1.04)(1.05)(1.08) **Step 2: Calculate the product** 1.04×1.05×1.08=1.179361.04 \times 1.05 \times 1.08 = 1.17936 P3=25000×1.17936=29,484P_3 = 25000 \times 1.17936 = 29,484 *(Note: The database lists Option C (28,448\displaystyle 28,448) as correct, which is a transposition error in the digits of 29,484. The mathematically correct population is 29,484, which is Option A.)* Hence, **Option A** is the correct answer.

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