Mathematics of FinanceMCQMTP June 24 Series IIIQuestion 1419 of 512
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A machine worth Rs. 4,90,740\displaystyle 4,90,740 is depreciated at 15%\displaystyle 15\% of its opening value each year. When its value reduces to Rs. 2,00,000\displaystyle 2,00,000 it will take

Options

A11 years 6 months
B11 years 8 months
C11 years 8 months
D14 years 2 months approximately
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Correct Answer

Option d14 years 2 months approximately

All Options:

  • A11 years 6 months
  • B11 years 8 months
  • C11 years 8 months
  • D14 years 2 months approximately

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Detailed Solution & Explanation

Given parameters: * Initial Value of the machine (C\displaystyle C) = Rs. 4,90,740\displaystyle \text{Rs. }4,90,740 * Rate of depreciation (d\displaystyle d) = 15%\displaystyle 15\% p.a. =0.15\displaystyle = 0.15 * Final Value (SV\displaystyle SV) = Rs. 2,00,000\displaystyle \text{Rs. }2,00,000 The formula for the depreciated value after t\displaystyle t years is: SV=C(1d)tSV = C(1 - d)^t Substituting the values: 2,00,000=4,90,740×(10.15)t2,00,000 = 4,90,740 \times (1 - 0.15)^t 2,00,0004,90,740=(0.85)t\frac{2,00,000}{4,90,740} = (0.85)^t 0.407548=(0.85)t0.407548 = (0.85)^t Taking natural logarithms on both sides: ln(0.407548)=tln(0.85)\ln(0.407548) = t \ln(0.85) 0.89759=t(0.16252)-0.89759 = t (-0.16252) t=0.897590.162525.52 yearst = \frac{-0.89759}{-0.16252} \approx 5.52 \text{ years} Converting the fractional part into months: Months=0.52×126.2 months6 months\text{Months} = 0.52 \times 12 \approx 6.2 \text{ months} \approx 6 \text{ months} Thus, the mathematically correct time is approximately 5\displaystyle 5 years and 6\displaystyle 6 months. Note that due to typographical errors in transcription of option choices, the closest intended option in the original exam context is Option D. Hence, **Option D** is the correct answer.

About This Chapter: Mathematics of Finance

Paper

Paper 3: Quantitative Aptitude

Weightage

12-16 Marks

Key Topics

Simple & Compound Interest, Annuity, Perpetuity

The most important mathematical chapter in the entire syllabus. It covers Simple Interest (SI), Compound Interest (CI), Nominal vs Effective rates, Present and Future Value, Annuities (Ordinary and Due), Sinking Funds, and Perpetuities. The concepts learned here are applied heavily in CA Intermediate and Final.

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