Mathematics for FinanceMTP June 24 Series IIQuestion 1535 of 512
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Arslan invested 10,000\displaystyle 10,000 at 8%\displaystyle 8\% per annum compound quarterly, then the value of the investment after 2\displaystyle 2 years is

Options

A11,716.59\displaystyle 11,716.59
B10,716.59\displaystyle 10,716.59
C11,716.59\displaystyle 11,716.59
DNone of these
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Correct Answer

✅ Option c — 11,716.59\displaystyle 11,716.59

All Options:

  • A11,716.59\displaystyle 11,716.59
  • B10,716.59\displaystyle 10,716.59
  • C11,716.59\displaystyle 11,716.59
  • DNone of these

Detailed Solution & Explanation

The value of the investment (A\displaystyle A) after compounding quarterly is: A=P(1+rm)m⋅nA = P \left(1 + \frac{r}{m}\right)^{m \cdot n} Given: * Principal (P\displaystyle P) = 10,000\displaystyle 10,000 * Nominal rate (r\displaystyle r) = 8%\displaystyle 8\% p.a. = 0.08\displaystyle 0.08 * Compounding frequency (m\displaystyle m) = 4\displaystyle 4 (quarterly) * Time (n\displaystyle n) = 2\displaystyle 2 years Substituting the values: A=10,000(1+0.084)4×2=10,000×(1.02)8A = 10,000 \left(1 + \frac{0.08}{4}\right)^{4 \times 2} = 10,000 \times (1.02)^8 Using (1.02)8≈1.171659\displaystyle (1.02)^8 \approx 1.171659: A=10,000×1.171659=11,716.59A = 10,000 \times 1.171659 = 11,716.59 This matches Option C. Hence, **Option C** is the correct answer.

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