Mathematics for FinanceMTP Jun 23 Series IIQuestion 1385 of 512
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1,25,000\displaystyle 1,25,000 is borrowed at compound interest at the rate of 2%\displaystyle 2\% for the 1\displaystyle 1st year, 3%\displaystyle 3\% for the 2\displaystyle 2nd year and 4%\displaystyle 4\% for the 3\displaystyle 3rd year. Find the amount to be paid after 3\displaystyle 3 years

Options

A125678\displaystyle 125678
B136587\displaystyle 136587
C163378\displaystyle 163378
D136578\displaystyle 136578
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Correct Answer

✅ Option d — 136578\displaystyle 136578

All Options:

  • A125678\displaystyle 125678
  • B136587\displaystyle 136587
  • C163378\displaystyle 163378
  • D136578\displaystyle 136578

Detailed Solution & Explanation

**Derivation of Compound Interest Value** Given: - Principal (P\displaystyle P) = Rs. 1,25,000\displaystyle \text{Rs. }1,25,000 - Rates for successive years: r1=2%\displaystyle r_1 = 2\%, r2=3%\displaystyle r_2 = 3\%, r3=4%\displaystyle r_3 = 4\% - Time (t\displaystyle t) = 3\displaystyle 3 years **Step 1: Set up the compound interest formula with varying rates** A=P(1+r1)(1+r2)(1+r3)A = P(1 + r_1)(1 + r_2)(1 + r_3) A=125000(1+0.02)(1+0.03)(1+0.04)A = 125000(1 + 0.02)(1 + 0.03)(1 + 0.04) A=125000(1.02)(1.03)(1.04)A = 125000(1.02)(1.03)(1.04) **Step 2: Calculate the product** 1.02×1.03×1.04=1.0926241.02 \times 1.03 \times 1.04 = 1.092624 A=125000×1.092624=Rs. 1,36,578A = 125000 \times 1.092624 = \text{Rs. }1,36,578 Hence, **Option D** is the correct answer.

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