Buying a note that is late in it's straight line amortization schedule

[Ben Bakhshi]

With straight line amortization schedules, interest payments decline over the life of the loan.

Does anyone have some tips (or formulas, or excel tables) for calculating the actual interest collected if you buy a note X years into Y term based on straight line amortization.

Buying a "mature" note, the buyer may end up collect much less interest than on paper.

[Dion DePaoli]

A Linear Amortization schedule is where the principal is fixed and the Interest varies on top of the fixed principal amount due each period.  The principal due each period is simply the principal loan amount divided by the term.  The interest due is then calculated based on the remaining balance each period.  

Taking this loan at a discount would simply mean that discounted portion of the fixed principal due each period is now a part of your interest income.  Since in the loan schedule it is fixed for the Borrower, it would be fixed for the investor as well.

The interest is always the highest in the beginning of any loan term because the total amount of principal due is at the greatest outstanding balance.  If you Borrower $100k at 5% interest over 30 years the linear principal is $277.78 every period for 360 periods.  It never changes.  

To find the interest we can do (Loan Balance x Interest Rate%)/12.  The interest in period 1 would be $416.  The interest in period 2 would be $415....etc.  The total payment due is $694.44 in period 1 and $693.29 in period 2.  So the payments for the Borrower would decline since the interest is a variable added on top of the principal each period after the previous periods principal reduction (fixed amount) is applied.  

So, if the Borrower pays $277.78 in principal each month and the loan has 250 payments remaining the balance has been reduced by $30,555.56.  So the current balance should be $69,444.44.  If you purchase that same loan for a $19,444.44 discount or $50k then you can apply the same linear metric to your discount since it is the principal portion of the loan.  So we take $19,444.44 divided by the Remaining Term (250) for $77.78.  Which means what ever the interest is each period we can add $77.78 to it to figure out our investment's interest income.  In this example the Investor's interest income would be $367.13 ($77.78+$289.35).  The Borrower's payment that period is $567.13 ($277.78+$289.35) for reference.

It would not be common for the principal portion of the payment and the interest portion of the payment to be the same unless the loan was short in term or small in principal.  Even then, it would only be the [exact] same in a very few scenarios.  Just not the way that math would really work.  So, if that is a result you are getting check your math, doesn't sound correct.  

Buying a near maturity Linear Mortgage would not affect the rate of interest or yield for the investor without any prepayment.  The interest charge is the interest charged based on the principal balance each period.  So unless the principal is prepaid the balance would only be $277.78 less than last period and the interest charged would on the remaining balance would be 5%.  As such, the same would go for your discount of $77.78.  Nothing changed the interest due on the account and the only thing that could change it is the interest rate changes or the balance to which the interest is applied changes.  

Now a post maturity asset would have some issues most likely.  If maturity has come and gone and there is a balance remaining you need to really look at the accounting.  If the matter is a function of missed payments then an extension of the number of missed payments should produce the original plan of paying to zero in X number of payments.  If for some reason that does not line up, then you will have to see if the Mortgagee miss applied the amounts due in some past periods and thus caused the Unpaid Principal Balance to fall off schedule.   I can't off the top of my head think of too many reasons why this would happen.  These are fairly straight forward applications of payment but strange things happen.  

Any of these Linear Mortgages with a matching interest rate, balance and matching remaining term would be equal regardless of the vintage or age of the loan.  All the math would be the same because all the numbers are the same.  Primarily a function of the linear method of reducing the principal due.