The following is an excerpt from an email I received from a client:
We calculated a loan in NLS using the following contract terms:
NLS is calculating the right monthly payment. However, total loan interest (Finance Charge) does not match the contract's $10,984.49.
The difference is the $18.63 that was adjusted by NLS on the final payment (see NSL amortization schedule).
What setting do we need to change in NLS to agree to the $10,984.49?
Here is the answer I provided to this client:
This is an interesting question. It is an easy one to answer, but it may be harder to answer it to your satisfaction.
The finance charge on the TILA is an approximation. The one on NLS is not.
Now, I'm not going to leave it at that. I'm going to mathematically prove this to you, and once we have accepted this premise, you will see that any attempt to make the interest projection in NLS match the Finance Charge on the TILA is a "fallacy of false cause," or alternatively one could call it a "strawman argument." Bottom line, you don't want to try to match that finance charge.
Here is the fallacy: NLS has calculated the interest over the life of the loan by using our amortization schedule to walk the loan forward to its maturity, with the assumption that all payments are made on time. When we get to the final payment on the maturity date, we reduce the final payment to the current payoff balance of the loan (which you must legally do on this loan type). The other program has NOT done an amortization schedule to see what the payoff balance is when we get to the final payment and has therefore simply ASSUMED that the final payment will be the same as all the others. This is allowed on a TILA because of the recognition of the fact that the amortization schedule changes every time that the borrower is as much as one day early or late with a payment. (As they say in the military, no plan survives contact with the enemy.) Given that the amortization schedule will probably not be followed exactly, and never will in practice unless in the case of a loan where automatic payments are set up and there is never an NSF, Reg Z allows the Finance Charge on the TILA to be an approximation. When I show you how they calculated it in the TILA disclosure that you sent me, it should be clear that this is the case.
Here is the proof:
1) You have stipulated that NLS has the same monthly payment, so we will take it as given that this payment amount is correct. This is $429.56
2) The term is 60 payments.
3) $429.56 x 60 = $25,773.60. Notice that this is the number that they have shown on the TILA for "Total of Payments." Clearly, they have ASSUMED that the final payment will be exactly the same amount as all of the other payments. This is almost never true, and they know it, but remember, our NLS calculation for the final payment will only be the case if all payments are made exactly on the due date. If you use the payment amount that comes from "amortize based on actual interest year," and get the "best fit payment" for the terms in question, the probability of the final payment being the same on a 60-payment loan is about 1.66%, so we can be pretty sure that no amortization schedule was run to get this number. It is simply the product of the monthly payment times the number of payments.
4) The amount financed is $14,789.11.
5) $25,773.60 - 14,789.11 = $10,984.49. There is our total finance charge. It is no more or less accurate than the Total of Payments. Once we accept the fact that the final payment WILL be some number other than $429.56, it naturally follows that this is an approximation. The one in NLS is NOT an approximation.
Now, we can easily prove the calculations in the NLS amortization schedule with a hand calculator but doing it for all 60 payments would be a time-consuming process. If it was easy, then you would be using the hand calculator loan system instead of NLS. I suggest that you use the calculator to verify the breakdown of the first four or five payments to get a level of confidence in how that amortization schedule is derived, and then once you have that faith, you would gain acceptance of the number at the end of the amortization schedule.
While I am telling you that the NLS amortization schedule is correct given the settings of the loan that you have in NLS, I cannot tell you that you have the correct settings for your loan. This is mostly affected by the interest year setting you are using. For example, ACT/360 will have the highest yield and could get you closer to the number in the TILA. But to tell you which interest year is correct, I would not look to the TILA approximation of finance charge, because I know they didn't do a rigorous calculation. I would look for a paragraph in the loan contract that usually falls somewhere on the upper portion of the second page and usually begins with words like "Interest shall be calculated based on…" Reading this, I can tell you which interest year calculation is contractually correct. I cannot tell you if you have the right settings in the program that was used to generate the TILA for the comparison.
I hope that this explanation was helpful, and we would be happy to help further with determining which interest year is correct and which settings will give you the contractually correct configuration for your loans, but this is predicated on the assumption that we must discard the notion that we should be matching something, which we know (and now you know) to NOT be a precise calculation.