Mathematics for FinanceMTP Dec 23 Series IQuestion 1393 of 512
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The Compounded interest Rs.8000\displaystyle 8000 for 6\displaystyle 6 months at 12%\displaystyle 12\% p.a payable quarterly is

Options

ARs.487.20\displaystyle 487.20
BRs.480\displaystyle 480
CRs.380\displaystyle 380
DNone of these
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Correct Answer

✅ Option a — Rs.487.20\displaystyle 487.20

All Options:

  • ARs.487.20\displaystyle 487.20
  • BRs.480\displaystyle 480
  • CRs.380\displaystyle 380
  • DNone of these

Detailed Solution & Explanation

**Derivation of Compound Interest** Given: - Principal (P\displaystyle P) = Rs. 8,000\displaystyle \text{Rs. }8,000 - Nominal rate (r\displaystyle r) = 12%\displaystyle 12\% per annum - Compounding Frequency = Payable quarterly (m=4\displaystyle m = 4) - Time (t\displaystyle t) = 6\displaystyle 6 months = 0.5\displaystyle 0.5 years **Step 1: Calculate periodic rate (i\displaystyle i) and total compounding periods (n\displaystyle n)** - Periodic rate i=r4=12%4=3%=0.03\displaystyle i = \frac{r}{4} = \frac{12\%}{4} = 3\% = 0.03 - Total compounding periods n=t×4=0.5×4=2\displaystyle n = t \times 4 = 0.5 \times 4 = 2 quarters **Step 2: Calculate the future value (A\displaystyle A)** A=P(1+i)nA = P(1 + i)^n A=8000(1+0.03)2A = 8000(1 + 0.03)^2 A=8000(1.03)2A = 8000(1.03)^2 A=8000×1.0609=Rs. 8,487.20A = 8000 \times 1.0609 = \text{Rs. }8,487.20 **Step 3: Calculate the Compound Interest (CI\displaystyle CI)** CI=A−P=8487.20−8000=Rs. 487.20CI = A - P = 8487.20 - 8000 = \text{Rs. }487.20 Hence, **Option A** is the correct answer.

More Questions from Mathematics for Finance

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If Rs. 1,000\displaystyle \text{Rs. }1,000 be invested at interest rate of 5%\displaystyle 5\% and the interest be added to the principal every 10\displaystyle 10 years, then the number in years in which it will amount to Rs. 2,000\displaystyle \text{Rs. }2,000 is:

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