Mathematics for FinancePYQ Nov 19Question 1201 of 512
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The value of scooter is Rs. 10,000\displaystyle \text{Rs. }10,000 find its value after 7\displaystyle 7 years if rate of depreciation is 10%\displaystyle 10\% p.a.

Options

ARs. 4,782.96\displaystyle \text{Rs. }4,782.96
BRs. 4,278.69\displaystyle \text{Rs. }4,278.69
CRs. 42,079\displaystyle \text{Rs. }42,079
DRs. 42,000\displaystyle \text{Rs. }42,000
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Correct Answer

✅ Option a — Rs. 4,782.96\displaystyle \text{Rs. }4,782.96

All Options:

  • ARs. 4,782.96\displaystyle \text{Rs. }4,782.96
  • BRs. 4,278.69\displaystyle \text{Rs. }4,278.69
  • CRs. 42,079\displaystyle \text{Rs. }42,079
  • DRs. 42,000\displaystyle \text{Rs. }42,000

Detailed Solution & Explanation

**Derivation of Depreciated Value** Given: - Initial Value of Scooter (V0\displaystyle V_0) = Rs. 10,000\displaystyle \text{Rs. }10,000 - Rate of Depreciation (d\displaystyle d) = 10%\displaystyle 10\% per annum - Time (t\displaystyle t) = 7\displaystyle 7 years **Step 1: Set up the depreciation formula** Vt=V0(1−d)tV_t = V_0(1 - d)^t V7=10000(1−0.10)7V_7 = 10000(1 - 0.10)^7 V7=10000(0.9)7V_7 = 10000(0.9)^7 **Step 2: Compute the value** (0.9)7≈0.4782969(0.9)^7 \approx 0.4782969 V7=10000×0.4782969=Rs. 4,782.969≈Rs. 4,782.96V_7 = 10000 \times 0.4782969 = \text{Rs. }4,782.969 \approx \text{Rs. }4,782.96 Hence, **Option A** is the correct answer.

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