Mathematics for FinancePYQ Jun 23Question 1466 of 512
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A car is available for 4,98,200\displaystyle 4,98,200 cash payment or 60,000\displaystyle 60,000 cash down payment followed by three equal annual instalments. If the rate of interest charged is 14%\displaystyle 14\% per annum compounded yearly, then total interest charged in the instalment plan is (Given P(2.0,14)=2.32163\displaystyle P(2.0,14) = 2.32163):

Options

A1,46,314\displaystyle 1,46,314
B1,46,137\displaystyle 1,46,137
C1,28,040\displaystyle 1,28,040
D1,58,040\displaystyle 1,58,040
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Correct Answer

✅ Option a — 1,46,314\displaystyle 1,46,314

All Options:

  • A1,46,314\displaystyle 1,46,314
  • B1,46,137\displaystyle 1,46,137
  • C1,28,040\displaystyle 1,28,040
  • D1,58,040\displaystyle 1,58,040

Detailed Solution & Explanation

Given parameters: * Initial Value (C\displaystyle C) = Rs. 10,00,000\displaystyle \text{Rs. }10,00,000 * Rate of depreciation (d\displaystyle d) = 10%\displaystyle 10\% p.a. =0.10\displaystyle = 0.10 * Time (n\displaystyle n) = 10\displaystyle 10 years The Scrap Value (SV\displaystyle SV) after depreciation is given by: SV=C(1−d)nSV = C(1 - d)^n Substituting the values: SV=10,00,000×(1−0.10)10SV = 10,00,000 \times (1 - 0.10)^{10} SV=10,00,000×(0.9)10SV = 10,00,000 \times (0.9)^{10} First, let's calculate (0.9)10\displaystyle (0.9)^{10}: (0.9)10≈0.34867844(0.9)^{10} \approx 0.34867844 Now substitute this back: SV=10,00,000×0.34867844=3,48,678.44SV = 10,00,000 \times 0.34867844 = 3,48,678.44 Thus, the scrap value is Rs. 3,48,678.44\displaystyle \text{Rs. }3,48,678.44. (Note: While some keys mark Option B, Option A is the mathematically correct value). Hence, **Option A** is the correct answer.

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