Mathematics for FinancePYQ June 22Question 1234 of 512
All Questions

The effective rate of interest corresponding to a nominal rate of 7%\displaystyle 7\% p.a. convertible quarterly.

Options

A7%\displaystyle 7\%
B7.5%\displaystyle 7.5\%
C5%\displaystyle 5\%
D7.18%\displaystyle 7.18\%
For any discrepancies in this question, email contact@cadada.in

Correct Answer

✅ Option d — 7.18%\displaystyle 7.18\%

All Options:

  • A7%\displaystyle 7\%
  • B7.5%\displaystyle 7.5\%
  • C5%\displaystyle 5\%
  • 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: Use the effective rate of interest (E\displaystyle E) formula** 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.

More Questions from Mathematics for Finance

Ready to Master Mathematics for Finance?

Practice all 512 questions with instant feedback, earn XP, track your streaks, and ace your CA Foundation exam.

Start Practicing — It's Free