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The effective annual rate of interest corresponding to a nominal rate of 6% per annum payable half-yearly is: 
  • a)
    6.07%
  • b)
    6.08%
  • c)
    6.06%
  • d)
    6.09%
Correct answer is option 'D'. Can you explain this answer?
Verified Answer
The effective annual rate of interest corresponding to a nominal rate ...
Amount of Rs. 100 for 1 year
when compounded half-yearly = Rs.[100*(1+3/100)^2]=Rs.106.09
Effective rate=(106.09-100)%=6.09%
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The effective annual rate of interest corresponding to a nominal rate ...
Calculation of Effective Annual Rate of Interest:

Step 1: Find the half-yearly rate of interest (i)

Given, Nominal rate of interest (r) = 6% per annum payable half-yearly

Therefore, the half-yearly rate of interest (i) = r/2 = 6/2 = 3% per half-year

Step 2: Calculate the effective annual rate of interest (EAR)

Using the formula:

(1 + i)^n - 1

EAR = ------------------
n

where n is the number of compounding periods per year

Given, the nominal rate of interest is compounded half-yearly

So, n = 2

Substituting the values, we get:

(1 + 0.03)^2 - 1
EAR = ----------------- = 0.0609 or 6.09%
2

Therefore, the effective annual rate of interest corresponding to a nominal rate of 6% per annum payable half-yearly is 6.09%.

Hence, option D is the correct answer.
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The effective annual rate of interest corresponding to a nominal rate ...
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The effective annual rate of interest corresponding to a nominal rate of 6% per annum payable half-yearly is:a)6.07%b)6.08%c)6.06%d)6.09%Correct answer is option 'D'. Can you explain this answer?
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