Final answer:
The equivalent annual rate (EAR) for a mortgage interest rate of 5.54% per year, compounded semiannually, is approximately 5.66% when compounded annually.
Step-by-step explanation:
The student has asked for the equivalent annual rate (EAR) when a mortgage interest rate is given as 5.54% per year, compounded semiannually. To find this, we convert the semiannual rate to an annual rate by using the formula EAR = (1 + r/n)^(n) - 1, where r is the nominal annual interest rate and n is the number of compounding periods per year. In this case, r = 5.54% or 0.0554, and n = 2 (since interest is compounded semiannually).
So the calculation is EAR = (1 + 0.0554/2)^(2) - 1 = (1 + 0.0277)^(2) - 1 = 1.05660249 - 1 = 0.05660249 or approximately 5.6602%. Thus, the equivalent annual rate compounded annually for a rate of 5.54% compounded semiannually is roughly 5.66%.