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Do the days in the month play a role when the interest rate is compounded Semi-Annually?
An example given to me
I haven't ever seen an interest paid increase while payments are made. Usually they are always decreasing.
Yes; the lender has chosen to convert the nominal interest rate to an equivalent daily rate, and to then compound this for each day of the period between payments.
The calculation goes like this:
8.5% compounded semi-annually, is converted into an effective annual rate: (1+0.0425)^2, or an effective annual rate of 8.680625%
Then calculate the equivalent daily rate: (1.08680625)^(1/365), or a daily rate of 0.022808998% per day. Finally, to calculate the interest for Feb 15 to Mar 15:
(1+0.00022808998)^28 - 1, then multiply by the Feb 15 principal...
The difference is that the exponent on the daily rate has to change for each month, and for leap-years...
It's basically sort of fair, but it usually results in a tiny bit more for the lender...
