Mathematics for FinanceMTP Mar 22/ RTP Sep 24Question 1351 of 512
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If 10,000\displaystyle 10,000 is invested at 8%\displaystyle 8\% per annum, then compounded quarterly. Then value of investment after 2\displaystyle 2 years is.

Options

A11,716.59\displaystyle 11,716.59
B10,716.59\displaystyle 10,716.59
C12,715.59\displaystyle 12,715.59
Dnone of these
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Correct Answer

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

All Options:

  • A11,716.59\displaystyle 11,716.59
  • B10,716.59\displaystyle 10,716.59
  • C12,715.59\displaystyle 12,715.59
  • Dnone of these

Detailed Solution & Explanation

**Derivation of Compound Interest Value** Given: - Principal (P\displaystyle P) = Rs. 10,000\displaystyle \text{Rs. }10,000 - Nominal Rate (r\displaystyle r) = 8%\displaystyle 8\% per annum compounded quarterly - Time (t\displaystyle t) = 2\displaystyle 2 years **Step 1: Calculate periodic rate (i\displaystyle i) and total periods (n\displaystyle n)** - Periodic rate i=r4=8%4=2%=0.02\displaystyle i = \frac{r}{4} = \frac{8\%}{4} = 2\% = 0.02 per quarter. - Total periods n=t×4=2×4=8\displaystyle n = t \times 4 = 2 \times 4 = 8 quarters. **Step 2: Calculate the future value (A\displaystyle A)** A=P(1+i)nA = P(1 + i)^n A=10000(1+0.02)8A = 10000(1 + 0.02)^8 A=10000(1.02)8A = 10000(1.02)^8 Using (1.02)8≈1.171659\displaystyle (1.02)^8 \approx 1.171659: A=10000×1.171659=Rs. 11,716.59A = 10000 \times 1.171659 = \text{Rs. }11,716.59 Hence, **Option A** is the correct answer.

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