The effective annual rate of interest corresponding to a nominal rate of 6% per annum payable half-yearly is:A)6.06%B)6.07%C)6.0B%D)6.09%
Question
The effective annual rate of interest corresponding to a nominal rate of 6% per annum payable half-yearly is:A)6.06%B)6.07%C)6.0B%D)6.09%
Solution
The effective annual rate (EAR) can be calculated using the formula:
EAR = (1 + i/n)^(nt) - 1
where: i = nominal interest rate n = number of compounding periods per year t = number of years
In this case, the nominal interest rate (i) is 6% or 0.06 (in decimal form), the number of compounding periods per year (n) is 2 (since it's compounded semi-annually), and the number of years (t) is 1.
Substituting these values into the formula, we get:
EAR = (1 + 0.06/2)^(2*1) - 1 EAR = (1.03)^2 - 1 EAR = 1.0609 - 1 EAR = 0.0609
Converting this back to a percentage, the effective annual rate is 6.09%.
So, the correct answer is D) 6.09%.
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