Mathematics for FinanceMTP Nov 20Question 1309 of 512
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What is the sum of money will amount to 1035.50\displaystyle 1035.50 in four years at compound interest for 1\displaystyle 1st, 2\displaystyle 2nd, 3\displaystyle 3rd and 4\displaystyle 4th years being 4%\displaystyle 4\%, 3%\displaystyle 3\%, 2%\displaystyle 2\% and 1%\displaystyle 1\% respectively?

Options

A10,000\displaystyle 10,000
B11,000\displaystyle 11,000
C1035\displaystyle 1035
D11305\displaystyle 11305
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Correct Answer

✅ Option a — 10,000\displaystyle 10,000

All Options:

  • A10,000\displaystyle 10,000
  • B11,000\displaystyle 11,000
  • C1035\displaystyle 1035
  • D11305\displaystyle 11305

Detailed Solution & Explanation

**Derivation of Principal Amount** *Note: The question contains a typo in the amount value, stating it is 1035.50 instead of 11,035.50. We show the calculation using the correct amount of 11,035.50 which yields a matching option.* Given: - Future Value (A\displaystyle A) = Rs. 11,035.50\displaystyle \text{Rs. }11,035.50 - Time (t\displaystyle t) = 4\displaystyle 4 years - Compound interest rates: r1=4%\displaystyle r_1 = 4\%, r2=3%\displaystyle r_2 = 3\%, r3=2%\displaystyle r_3 = 2\%, r4=1%\displaystyle r_4 = 1\% **Step 1: Set up the formula for compound interest with varying rates** A=P×(1+r1)(1+r2)(1+r3)(1+r4)A = P \times (1 + r_1)(1 + r_2)(1 + r_3)(1 + r_4) 11035.50=P×(1+0.04)(1+0.03)(1+0.02)(1+0.01)11035.50 = P \times (1 + 0.04)(1 + 0.03)(1 + 0.02)(1 + 0.01) 11035.50=P×(1.04×1.03×1.02×1.01)11035.50 = P \times (1.04 \times 1.03 \times 1.02 \times 1.01) **Step 2: Compute the product** 1.04×1.03×1.02×1.01=1.103550241.04 \times 1.03 \times 1.02 \times 1.01 = 1.10355024 11035.50=1.10355024P11035.50 = 1.10355024 P **Step 3: Solve for P\displaystyle P** P=11035.501.10355024≈Rs. 10,000P = \frac{11035.50}{1.10355024} \approx \text{Rs. }10,000 *(If we use the literal question amount of 1035.50: P=1035.501.10355024≈938.33\displaystyle P = \frac{1035.50}{1.10355024} \approx 938.33.)* Hence, **Option A** is the correct answer.

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