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Today someone showed me a SallieMae statement and told me that she pay a fixed amount, 300 dollars, every month for her student loan and ask me why the amount applied to the principal of the loan is different every month. In order to show her I really have an MBA degree I spend a couple hours to do calculation in excel to figure it out and explain it to her.

Basically her Aug, Sept and Oct statements looks like the following. From the statements you can see that

she paid $300 every month to her loan. From Aug 17th to Sept 17th the outstanding principal dropped $260.74 and from Sept 17 to Oct 17 the outstanding principal dropped 254.43. So how come outstanding principal didn’t decrease in the same amount. The reason for that is pretty simple. The banks accrue interest on a daily bases and since she usually paid her loan on a different day every month. The interest accrued was different for every pay interval. Whenever a payment was made it was used to cover the interest accrued first and after that the rest of the payment was applied to the principal.

For example on her case the outstanding principal on 9/17/2007 statement was $12865.81 and her last payment before 9/17/2007 was on 8/27/2007. That means the payment on 8/27/2007 brought her outstanding principle down to $12865.81 and starting on 8/27/2007 her interest was accrued on the amount of $12865.81. So let us calculate the interest accrued from 8/27/2007 to the day she made the next payment, which was on 10/11/2007.

There were 45 days between the two payments and the daily interest rate was 2.875% / 365 = 0.007877%. Interest accrued was calculated as
$12865.81 * ((1+0.007877%) ^ 45 - 1) = $45.68

Now she paid $300 on 10/11/2007. Among the payment $45.68 was used to pay off the interest accrued. The rest of it $300 - $45.68 = $254.32 was applied to the principal. There was small discripency. The statement showed that principal was brought down by $254.43. Most likely it was due to rounding.

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