Mathematics for FinanceMTP Sep 24 Series IQuestion 3957 of 507
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The Compound interest 8000\displaystyle 8000 for 6\displaystyle 6 months at 12%\displaystyle 12\% p.a payable quarterly is:

Options

A487.20\displaystyle 487.20
B480\displaystyle 480
C380\displaystyle 380
DNone of these
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Correct Answer

✅ Option a — 487.20\displaystyle 487.20

All Options:

  • A487.20\displaystyle 487.20
  • B480\displaystyle 480
  • C380\displaystyle 380
  • DNone of these

Detailed Solution & Explanation

Given parameters: * Principal (P\displaystyle P) = Rs. 8,000\displaystyle \text{Rs. }8,000 * Nominal Interest Rate (r\displaystyle r) = 12%\displaystyle 12\% p.a. * Time (t\displaystyle t) = 6\displaystyle 6 months = 0.5\displaystyle 0.5 years Since the interest is compounded quarterly: * Number of conversion periods per year (m\displaystyle m) = 4\displaystyle 4 * Quarterly interest rate (i\displaystyle i) = 12%4=3%=0.03\displaystyle \frac{12\%}{4} = 3\% = 0.03 * Total number of conversion periods (n\displaystyle n) = t×m=0.5×4=2\displaystyle t \times m = 0.5 \times 4 = 2 quarters The formula for compound amount is: A=P(1+i)nA = P(1+i)^n Substituting the values: A=8,000×(1.03)2A = 8,000 \times (1.03)^2 A=8,000×1.0609=8,487.20A = 8,000 \times 1.0609 = 8,487.20 The Compound Interest (CI\displaystyle CI) is: CI=A−P=8,487.20−8,000=487.20CI = A - P = 8,487.20 - 8,000 = 487.20 Thus, the compound interest is Rs. 487.20\displaystyle \text{Rs. }487.20. Hence, **Option A** is the correct answer.

Key Concepts to Understand

Compound Interest

Interest calculated on the initial principal, which also includes all of the accumulated interest of previous periods.

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