Mathematics for FinancePYQ Sep 24Question 1482 of 512
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What is the annual contribution required by an organization to accumulate 20,00,000\displaystyle 20,00,000 in ten years for the construction of a new manufacturing plant, utilizing a sinking fund with 8%\displaystyle 8\% annual interest rate of 8%\displaystyle 8\% compounded annually? (Where A(10,0.06)=13.180785\displaystyle A(10,0.06) = 13.180785)

Options

A1,67,440.90\displaystyle 1,67,440.90
B1,51,736.03\displaystyle 1,51,736.03
C1,75,433.60\displaystyle 1,75,433.60
D1,83,714.28\displaystyle 1,83,714.28
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Correct Answer

✅ Option b — 1,51,736.03\displaystyle 1,51,736.03

All Options:

  • A1,67,440.90\displaystyle 1,67,440.90
  • B1,51,736.03\displaystyle 1,51,736.03
  • C1,75,433.60\displaystyle 1,75,433.60
  • D1,83,714.28\displaystyle 1,83,714.28

Detailed Solution & Explanation

The annual payment (A\displaystyle A) required for a sinking fund to accumulate a future sum FV\displaystyle FV is: A=FVFV factor=FVA(n,i)A = \frac{FV}{\text{FV factor}} = \frac{FV}{A(n, i)} Given: * Future sum (FV\displaystyle FV) = 20,00,000\displaystyle 20,00,000 * Time (n\displaystyle n) = 10\displaystyle 10 years * Using the given factor: A(10,0.06)=13.180785\displaystyle A(10, 0.06) = 13.180785 (which corresponds to 6%\displaystyle 6\% interest rate) Substituting the values: A=20,00,00013.180785≈1,51,736.03A = \frac{20,00,000}{13.180785} \approx 1,51,736.03 Thus, the annual contribution is approximately 1,51,736.03\displaystyle 1,51,736.03. Hence, **Option B** is the correct answer.

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