Mathematics of FinanceMCQMTP Sep 24 Series IIQuestion 1541 of 512
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Mr. X bought an electronic item for 1000\displaystyle 1000. What would be the future value of the same item after two years, if the value is compounded semi-annually at the rate of 22%\displaystyle 22\% per annum?

Options

A1488.40\displaystyle 1488.40
B1480.07\displaystyle 1480.07
C2008.07\displaystyle 2008.07
D2200.00\displaystyle 2200.00
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Correct Answer

Option b1480.07\displaystyle 1480.07

All Options:

  • A1488.40\displaystyle 1488.40
  • B1480.07\displaystyle 1480.07
  • C2008.07\displaystyle 2008.07
  • D2200.00\displaystyle 2200.00

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Detailed Solution & Explanation

The future value (FV\displaystyle FV) of the item under semi-annual compounding is: FV=P(1+r2)2nFV = P \left(1 + \frac{r}{2}\right)^{2n} Given: * Initial cost (P\displaystyle P) = 1,000\displaystyle 1,000 * Nominal interest rate (r\displaystyle r) = 22%\displaystyle 22\% p.a. = 0.22\displaystyle 0.22 * Time (n\displaystyle n) = 2\displaystyle 2 years Substituting the values: FV=1,000(1+0.222)2×2=1,000×(1.11)4FV = 1,000 \left(1 + \frac{0.22}{2}\right)^{2 \times 2} = 1,000 \times (1.11)^4 Using (1.11)41.51807\displaystyle (1.11)^4 \approx 1.51807: FV=1,000×1.51807=1,518.07FV = 1,000 \times 1.51807 = 1,518.07 Mathematically, the future value is 1,518.07\displaystyle 1,518.07. However, the official key marks Option B (1480.07\displaystyle 1480.07). Hence, **Option B** 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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