Mathematics for FinanceMTP Mar 22Question 1347 of 512
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Present value of a scooter is 7,290\displaystyle 7,290. Its value decreases every year by 10%\displaystyle 10\% then the 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 a — 10,000\displaystyle 10,000

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

**Derivation of Scooter Value 3 Years Ago** Given: - Present Value (Vt\displaystyle V_t) = Rs. 7,290\displaystyle \text{Rs. }7,290 - Time (t\displaystyle t) = 3\displaystyle 3 years - Rate of Depreciation (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 7290=V0(1−0.10)37290 = V_0(1 - 0.10)^3 7290=V0(0.9)37290 = V_0(0.9)^3 7290=0.729V07290 = 0.729 V_0 **Step 2: Solve for V0\displaystyle V_0** V0=72900.729=Rs. 10,000V_0 = \frac{7290}{0.729} = \text{Rs. }10,000 Hence, **Option A** is the correct answer.

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