Mathematics for FinanceMTP Mar 22Question 1348 of 512
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Find the effective rate of interest at 10%\displaystyle 10\% p.a when the interest is payable quarterly.

Options

A10.38%\displaystyle 10.38\%
B5%\displaystyle 5\%
C5.04%\displaystyle 5.04\%
D4%\displaystyle 4\%
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Correct Answer

✅ Option a — 10.38%\displaystyle 10.38\%

All Options:

  • A10.38%\displaystyle 10.38\%
  • B5%\displaystyle 5\%
  • C5.04%\displaystyle 5.04\%
  • D4%\displaystyle 4\%

Detailed Solution & Explanation

**Derivation of Effective Rate of Interest** Given: - Nominal interest rate (r\displaystyle r) = 10%\displaystyle 10\% per annum - Compounding Frequency = Quarterly (m=4\displaystyle m = 4) **Step 1: Find the quarterly interest rate (i\displaystyle i)** i=rm=10%4=2.5%=0.025 per quarteri = \frac{r}{m} = \frac{10\%}{4} = 2.5\% = 0.025 \text{ per quarter} **Step 2: Calculate the effective annual interest rate (E\displaystyle E)** E=(1+i)m−1E = (1 + i)^m - 1 E=(1+0.025)4−1E = (1 + 0.025)^4 - 1 E=(1.025)4−1E = (1.025)^4 - 1 E≈1.103813−1=0.103813 or 10.38%E \approx 1.103813 - 1 = 0.103813 \text{ or } 10.38\% Hence, **Option A** is the correct answer.

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