Mathematics for FinanceMTP June 24 Series IQuestion 1409 of 512
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The effective annual rate of interest corresponding to nominal rate 6%\displaystyle 6\% p.a. payable quarterly is:

Options

A6.14%\displaystyle 6.14\%
B6.07%\displaystyle 6.07\%
C6.08%\displaystyle 6.08\%
D6.09%\displaystyle 6.09\%
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Correct Answer

✅ Option a — 6.14%\displaystyle 6.14\%

All Options:

  • A6.14%\displaystyle 6.14\%
  • B6.07%\displaystyle 6.07\%
  • C6.08%\displaystyle 6.08\%
  • D6.09%\displaystyle 6.09\%

Detailed Solution & Explanation

Given parameters: * Nominal rate of interest (r\displaystyle r) = 6%\displaystyle 6\% p.a. =0.06\displaystyle = 0.06 * Compounding frequency (m\displaystyle m) = 4\displaystyle 4 (compounded quarterly) The quarterly interest rate (i\displaystyle i) is: i=rm=0.064=0.015i = \frac{r}{m} = \frac{0.06}{4} = 0.015 The formula for the effective annual rate of interest (E\displaystyle E) is: E=(1+i)m−1E = (1 + i)^m - 1 Substituting the values: E=(1+0.015)4−1E = (1 + 0.015)^4 - 1 E=(1.015)4−1E = (1.015)^4 - 1 Let's compute (1.015)4\displaystyle (1.015)^4: (1.015)2=1.030225(1.015)^2 = 1.030225 (1.015)4=(1.030225)2≈1.06136355(1.015)^4 = (1.030225)^2 \approx 1.06136355 Thus: E≈1.06136355−1=0.06136355=6.14%E \approx 1.06136355 - 1 = 0.06136355 = 6.14\% The effective annual rate of interest is approximately 6.14%\displaystyle 6.14\%. Hence, **Option A** is the correct answer.

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