Mathematics for FinanceMTP 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 b — 1480.07\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

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)4≈1.51807\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.

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