Mathematics for FinanceMTP May 18, ICAI SMQuestion 1485 of 512
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A sinking fund is created to redeem debentures worth 5,00,000\displaystyle 5,00,000 at the end of 25\displaystyle 25 years. How much provision each need to be made out of profits each year provided sinking fund investments can earn at 4%\displaystyle 4\% per annum

Options

A12,000\displaystyle 12,000
B12,040\displaystyle 12,040
C12,039\displaystyle 12,039
D12,035\displaystyle 12,035
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Correct Answer

✅ Option a — 12,000\displaystyle 12,000

All Options:

  • A12,000\displaystyle 12,000
  • B12,040\displaystyle 12,040
  • C12,039\displaystyle 12,039
  • D12,035\displaystyle 12,035

Detailed Solution & Explanation

The annual provision (A\displaystyle A) needed for the sinking fund is: A=FV[(1+i)n−1i]A = \frac{FV}{\left[ \frac{(1+i)^n - 1}{i} \right]} Given: * Future value (FV\displaystyle FV) = 5,00,000\displaystyle 5,00,000 * Time (n\displaystyle n) = 25\displaystyle 25 years * Interest rate (i\displaystyle i) = 4%\displaystyle 4\% p.a. = 0.04\displaystyle 0.04 Substituting the values: A=5,00,000[(1.04)25−10.04]A = \frac{5,00,000}{\left[ \frac{(1.04)^{25} - 1}{0.04} \right]} Using (1.04)25≈2.665836\displaystyle (1.04)^{25} \approx 2.665836: A=5,00,00041.6459≈12,005.98≈12,006A = \frac{5,00,000}{41.6459} \approx 12,005.98 \approx 12,006 This corresponds to Option A (12,000\displaystyle 12,000 in system records). Hence, **Option A** is the correct answer.

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