Mathematics for FinanceMTP Apr 21Question 1325 of 512
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The cost of machinery Rs.1,25,000\displaystyle 1,25,000 if its useful life estimated to the 20\displaystyle 20 years and the rate of depreciation of its cost is 10%\displaystyle 10\% p.a. Then scrap value of machinery is

Options

ARs.15,187\displaystyle 15,187
BRs.15,400\displaystyle 15,400
CRs.15,300\displaystyle 15,300
DRs.15,250\displaystyle 15,250
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Correct Answer

✅ Option a — Rs.15,187\displaystyle 15,187

All Options:

  • ARs.15,187\displaystyle 15,187
  • BRs.15,400\displaystyle 15,400
  • CRs.15,300\displaystyle 15,300
  • DRs.15,250\displaystyle 15,250

Detailed Solution & Explanation

**Derivation of Machine Scrap Value** Given: - Initial Cost (V0\displaystyle V_0) = Rs. 1,25,000\displaystyle \text{Rs. }1,25,000 - Estimated useful life (t\displaystyle t) = 20\displaystyle 20 years - Depreciation Rate (d\displaystyle d) = 10%\displaystyle 10\% per annum **Step 1: Set up the depreciation formula** Vt=V0(1−d)tV_t = V_0(1 - d)^t Vt=125000(1−0.10)20V_t = 125000(1 - 0.10)^{20} Vt=125000(0.9)20V_t = 125000(0.9)^{20} **Step 2: Compute the value** (0.9)20≈0.12157665(0.9)^{20} \approx 0.12157665 Vt=125000×0.12157665≈Rs. 15,197V_t = 125000 \times 0.12157665 \approx \text{Rs. }15,197 *(Note: Option A is listed as Rs. 15,187, which is closest to the mathematical value and matches the textbook's key. We accept Option A.)* Hence, **Option A** is the correct answer.

Key Concepts to Understand

Depreciation

Allocation of the cost of a tangible fixed asset over its useful life due to wear and tear, efflux of time, or obsolescence.

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