Mathematics for FinanceMTP June 22Question 1355 of 512
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The present value of a scooter is 7290\displaystyle 7290. The rate of depreciation is 10%\displaystyle 10\%. What was its value 3\displaystyle 3 years ago?

Options

A10000\displaystyle 10000
B10010\displaystyle 10010
C9990\displaystyle 9990
D12000\displaystyle 12000
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Correct Answer

✅ Option a — 10000\displaystyle 10000

All Options:

  • A10000\displaystyle 10000
  • B10010\displaystyle 10010
  • C9990\displaystyle 9990
  • D12000\displaystyle 12000

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.

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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