Mathematics for FinancePYQ May 19Question 1284 of 512
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The effective rate of interest for one year corresponding to a nominal at 7%\displaystyle 7\% rate of interest per annum convertible quarterly is

Options

A7%\displaystyle 7\%
B7.02%\displaystyle 7.02\%
C8%\displaystyle 8\%
D7.18%\displaystyle 7.18\%
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Correct Answer

✅ Option d — 7.18%\displaystyle 7.18\%

All Options:

  • A7%\displaystyle 7\%
  • B7.02%\displaystyle 7.02\%
  • C8%\displaystyle 8\%
  • D7.18%\displaystyle 7.18\%

Detailed Solution & Explanation

**Derivation of Effective Rate of Interest** Given: - Nominal interest rate (r\displaystyle r) = 7%\displaystyle 7\% per annum - Compounding Frequency = Convertible quarterly (m=4\displaystyle m = 4) **Step 1: Find the quarterly interest rate (i\displaystyle i)** i=rm=7%4=1.75%=0.0175 per quarteri = \frac{r}{m} = \frac{7\%}{4} = 1.75\% = 0.0175 \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+0.0175)4−1E = (1 + 0.0175)^4 - 1 E=(1.0175)4−1E = (1.0175)^4 - 1 **Step 3: Calculate the value** (1.0175)4≈1.071859(1.0175)^4 \approx 1.071859 E=1.071859−1=0.071859 or 7.1859%≈7.18%E = 1.071859 - 1 = 0.071859 \text{ or } 7.1859\% \approx 7.18\% Hence, **Option D** is the correct answer.

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