Mathematics of FinanceMCQPYQ 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 a1,46,314\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

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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(1d)nSV = C(1 - d)^n Substituting the values: SV=10,00,000×(10.10)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)100.34867844(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.

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.

View Official ICAI Syllabus

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