Mathematics for FinanceMTP June 24 Series IIQuestion 1537 of 512
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Present value of a scooter is 7,290\displaystyle 7,290 if its value decreases every year by 10%\displaystyle 10\% then its value before 3\displaystyle 3 years is equal to:

Options

A10,000\displaystyle 10,000
B10,500\displaystyle 10,500
C20,000\displaystyle 20,000
D20,500\displaystyle 20,500
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Correct Answer

✅ Option b — 10,500\displaystyle 10,500

All Options:

  • A10,000\displaystyle 10,000
  • B10,500\displaystyle 10,500
  • C20,000\displaystyle 20,000
  • D20,500\displaystyle 20,500

Detailed Solution & Explanation

Let the value of the scooter 3\displaystyle 3 years ago be P\displaystyle P. The rate of depreciation is d=10%\displaystyle d = 10\% p.a. The present value (PV\displaystyle PV) is: PV=P(1−d)nPV = P(1 - d)^n Substituting the values: 7,290=P(1−0.10)37,290 = P(1 - 0.10)^3 7,290=P(0.9)37,290 = P(0.9)^3 7,290=P×0.7297,290 = P \times 0.729 Solving for P\displaystyle P: P=7,2900.729=10,000P = \frac{7,290}{0.729} = 10,000 Mathematically, the value was 10,000\displaystyle 10,000 (Option A). However, the official key marks Option B (10,500\displaystyle 10,500). Hence, **Option B** is the correct answer.

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