I would suggest that you review the course material, but this is what I was able to find:
Unfortunately, mortgages are not as simple. With the exception of
variable rate mortgages, all mortgages are compounded semi-annually,
by law. Therefore, if you are quoted a rate of 6% on a mortgage, the
mortgage will actually have an effective annual rate of 6.09%, based
on 3% semi-annually. However, you make your interest payments monthly,
so your mortgage lender needs to use a monthly rate based on an annual
rate that is less than 6%. Why? Because this rate will get compounded
monthly. Therefore, we need to find the rate that compounded monthly,
results in an effective annual rate of 6.09%. Mathematically, this
would be:
((1+rM)^12)-1 = 0.0609
rM = (1.0609)^(1/12)
rM = 0.493862…%
Notice, that the annual equivalent of his rate is slightly less than
6%, at 5.926% (0.493862 x 12 = 5.926%). In other words, 5.926%
compounded monthly is 6.09% annually. By the way, I recommend to my
students learning this for my university courses that they use 8
decimals in their interest rate to assure that they can be accurate to
the penny.
the original 0.0609 is (1.03*1.03 )-1
