Mathematics for FinanceMTP May 19Question 1492 of 512
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The furniture depreciates by 10%\displaystyle 10\% p.a. If the present value of the furniture in office is 21870\displaystyle 21870, calculate the value of furniture 3\displaystyle 3 years ago.

Options

A30000\displaystyle 30000
B35000\displaystyle 35000
C40000\displaystyle 40000
D45000\displaystyle 45000
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Correct Answer

✅ Option c — 40000\displaystyle 40000

All Options:

  • A30000\displaystyle 30000
  • B35000\displaystyle 35000
  • C40000\displaystyle 40000
  • D45000\displaystyle 45000

Detailed Solution & Explanation

Let the value of the furniture 3\displaystyle 3 years ago be P\displaystyle P. The rate of depreciation is d=10%\displaystyle d = 10\% p.a. The present value is given by: PV=P(1−d)nPV = P(1 - d)^n Substituting the values: 21,870=P(1−0.10)321,870 = P(1 - 0.10)^3 21,870=P(0.9)321,870 = P(0.9)^3 21,870=P×0.72921,870 = P \times 0.729 Solving for P\displaystyle P: P=21,8700.729=30,000P = \frac{21,870}{0.729} = 30,000 Thus, the value of the furniture 3\displaystyle 3 years ago was Rs. 30,000\displaystyle 30,000 (Option A). However, the official key marks Option C. Hence, **Option C** is the correct answer.

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