Mathematics for FinancePYQ Nov 18Question 1436 of 512
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The value of furniture depreciates by 10%\displaystyle 10\% a year, it the present value of the furniture in an office is 21,870\displaystyle 21,870. Calculate the value of furniture 3\displaystyle 3 years ago

Options

A30,000\displaystyle 30,000
B35,000\displaystyle 35,000
C40,000\displaystyle 40,000
D50,000\displaystyle 50,000
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Correct Answer

✅ Option a — 30,000\displaystyle 30,000

All Options:

  • A30,000\displaystyle 30,000
  • B35,000\displaystyle 35,000
  • C40,000\displaystyle 40,000
  • D50,000\displaystyle 50,000

Detailed Solution & Explanation

Let the value of the furniture 3\displaystyle 3 years ago be P0\displaystyle P_0. Given parameters: * Present Value (PV\displaystyle PV) = Rs. 21,870\displaystyle \text{Rs. }21,870 * Rate of depreciation (d\displaystyle d) = 10%\displaystyle 10\% p.a. =0.10\displaystyle = 0.10 * Time (n\displaystyle n) = 3\displaystyle 3 years The formula for depreciated value is: PV=P0(1−d)nPV = P_0 (1 - d)^n Substituting the values: 21,870=P0(1−0.10)321,870 = P_0 (1 - 0.10)^3 21,870=P0(0.9)321,870 = P_0 (0.9)^3 21,870=P0×0.72921,870 = P_0 \times 0.729 Solving for P0\displaystyle P_0: P0=21,8700.729=30,000P_0 = \frac{21,870}{0.729} = 30,000 Thus, the value of the furniture 3\displaystyle 3 years ago was Rs. 30,000\displaystyle \text{Rs. }30,000. (Note: While Option B is marked as correct in some study keys, the exact calculation yields 30,000, which is Option A). Hence, **Option A** is the correct answer.

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