>>Which is why I didn't really get down and, ahem, do the math; I just eyeballed the saving (a singular saving - rare thing nowadays!) at about $20K in paying that mortgage in 33 months. Add a few thousand for the extra insurance we'd have to pay had we not been able to make 20% down payment. Now anyone calculate how many hours of work, at their own rate, would it take to earn this money, and what would it have bought, had I paid?
>
>For autos, a simple interest loan allows you to have a set low payment over the period of the loan. There are no penalties for early payoff or prepayment

Which would be ridiculous if it weren't preposterous - the whole reason for existence of interest is "you're paying for what the lender is losing by not investing that money into something more rewarding than you, ingrate!" (but then why doesn't he?). So the lender is supposedly suffering because his money is busy with you, so you have to pay for that; then you pay earlier to relieve his suffering, and you get penalized for that too.

>and you then don't pay the interest that would be paid over the life of the loan. No rule of 78s either where a lender typically collects 3/4s of the interest in the first half of a loan's payments (that is always in the fine print if it exists and in most states, the lendor has to mention it).

Now this is a nice example of hand calculation shortcut which then becomes nearly incomprehensible until you try to actually do it. Calculation of the monthly installment is actually iterative, which is why we have payment() function (and others), or else we'd have to code them each time. The 78s calculation is a shorthand way to do the same: apply one month's interest to the principal, take one installment off; apply next month's interest, deduce next installment etc etc. This method more or less assumes the interest will be what it was pre-calculated in advance, so it doesn't need to be accurately calculated at each payment. Given that this is just multiplication, although of long numbers, that sort of thing could have been done with mechanical crank machines - I remember my dad used to bring one home when he had too much work. It's just that the lender wanted to save workhours (and potential errors, plus time to fix them, plus potential lawsuit costs, maybe) so they applied this shortcut - which becomes inaccurate with the first early payment.

This cracks me up: "In the United States, the use of the Rule of 78s is prohibited in connection with mortgage refinancings and other consumer loans having a term exceeding 61 months." (from http://en.wikipedia.org/wiki/Rule_of_78s) - another case of "it's not bad per se, it's bad in certain cases, with exceptions... we won't make a real rule, just a list of cases when". Under 78s, I wouldn't reduce the interest on my car loan from $1000 to $600, I would have saved maybe only $150, and would probably have paid interest for those two extra months that it would take.

> It gives the flexibility of low payments when times are lean but allows for early payoff when times are good. If you pay more than the standard scheduled payment, the excess is applied to the principal and not interest.

This took me a while to digest. What interest if it's already paid? And then after reading about the 78s (*) I understood that these cheats were calculating interest on the paid part, in case you paid early, because they weren't really calculating it - it was calculated in advance, so anything out of schedule was irrelevant, the payment went on just the same. Which then meant that under that system I would have not seen the actual interest drop proportionally as I was decimating the principal.

Nowadays it's much simpler and no such schemes are needed - there's enough software written, and anyone with the simplest calculator can check the interest charged, at least for one month at a time.

> I think it is the most common type of auto loan here. I don't think there are many pre-computed auto loans, but then there could be and I am just not aware of how many.

There's no reason for pre-computed anymore, nor justification. There are just ossified habits. Pretty much like the city library back home, which was closing the membership book on 31st of december, and everybody had to enlist anew - and then kept this as a rule some twelve years after they got the whole book lending computerized (btw, one of my former enterprises did it - I was sort of still there then). Probably the old comrade lady finally threw the spoon or retired. Likewise, the loan payments could be a bit more flexible - one could be charged an amount as calculated on the day of payment. No matter whether they pay once in two months or once a week.

BTW, I once paid an additional sum, when it became available, and it was applied against the next month, with interest for the rest of the current month applied to it. Knowing what it would take to fix this, I just added this to my knowledge of how they operate (and this was a credit union, not a bank!) and maneuvered my payments around that behavior til the end.

Which brings me to a much more important point: the "you pay the interest first" and then displaying the interest in a separate column, and then designating the rest as a payment against the principal. This is a deliberate maneuver to make this all look as if there's no interest on interest, as if the interest is somehow never added to the principal - it's calculated, paid, gone, and then you are alone with the principal.

Well, wrong. The interest is expressed as an annual rate. But then we don't wait for the end of the year to charge it, do we? We charge each month. Which means we got our interest and can operate with it, invest it in the next loan right away, and get the next interest on it the very next month. So if we, the lien, are making interest on interest, the debtor is somehow supposed to believe that he isn't paying it? ;)

FOR rate=1 TO 12 STEP 0.25
	?rate, ((1+rate/(12*100))**12-1)*100
ENDFOR

This piece of code will show the difference between the nominal annual rate and the actual rate when a twelfth of it is applied twelve times (i.e. assuming that the interest is calculated and charged 12 times a year). Feel free to extend the loop to higher percentages, up to whatever credit card issues may charge if they really love you - 20%, 30% (ok, 19.99%, 29.99%). Becomes really interesting. Thousand small wounds.


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(*) "sum of digits" makes as much sense as "sum of ideograms" or "sum of traffic signs", because digits are alphabetic elements used for representation of numbers; they don't have a value by themselves, the single digit numbers associated with them do. So "sum of digits" is more a checksum technique, where one takes all the digits of a long number, as if they were single digit numbers, and sums them. Just shows (**) that even then, in the 30s when they made this calculation, they didn't ask mathematicians - probably because these would have gone to embrace the nearest porcelain.

(**) I could have written "goes to show", but if anyone asked me "goes where?", I wouldn't know what to say, so I didn't.