# Days in the month affecting loans?

Do the days in the month play a role when the interest rate is compounded Semi-Annually?

An example given to me

1. Interest rate of 8.5 compounded Semi-Annually, fixed
2. Blended payment of principal and interest
3. Payment fixed at \$1,289.15
4. Payment monthly
5. First payment March 15, 2014
6. Payment count type = end balance 0

http://snag.gy/RLUC8.jpg

I haven't ever seen an interest paid increase while payments are made. Usually they are always decreasing.

• did you even try to do the math? the daily cost of interest for each payment is 10.48;10.25;10.03;9.81: it drops 22 or 23 cents every month Mar 6, 2014 at 16:52

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...

• In many loan agreements in the US, an year is defined as 360 days consisting of 12 months of 30 days each for the purpose of computing the interest rate. Thus, the rate per month for interest compounded monthly is APR/12 while if compounding is daily, the daily rate is APR/360. Mar 7, 2014 at 3:53
• In many loan agreements, yes. However, the calculations in my answer above reproduce the OP's amortization schedule to the penny. Mar 7, 2014 at 4:31
• @User58220 Hi, By anychance would you happen to also know how to calculate the payment? Aug 1, 2014 at 16:24