Amortization Problem

General Questions
#1

Me and the wife recently purchased a new car, but because of our bad credit history we were stuck with a 17.9% APR and $450/mo. payments for the next 5 years…adds up to paying over $29,000 for a $17,000 car. No problem, we were assured that if we made a large payment later it would go off the principal, and 60% of the payments we made until then went towards the principal. I get a $17,000 check in June because my company was bought out and I had stock options, so I figured I’d pay it off then.

My wife was looking into the possibility of paying it off partially, so we could make a years worth of payments on it and improve our credit rating. She called the bank that financed it to see what size payment we would have to make to do this, get some ideas on what they payments might be reduced to, etc. She was told there was no way they could give them any information like that, the payment would have to be made first and then they could refer to their amortization tables to tell how many payments would be left. She was also told the payments would not be reduced, and if we payed $10,000 and reduced the principal to $5000 or so, the interest would not be reduced, we would continue to pay 40% of the payment towards interest until the principal was reduced to 0, which could take a couple of years.

This makes me kinda suspicious, especially the part about them not being able to tell you anything until after we had made the large payment. Is there anyone with financial training, experience with car finance, or just personal anecdotes who might be able to help me figure out what to do? I’m strongly tempted to say ‘screw improving my credit’ and pay off the whole principal in June, but my wife is against that. My second choice would be to pay all but $1350 of the principal, which SUPPOSEDLY would be paid off in my next 5 payments if that 60% figure is right, which would have us making exactly 12 payments on it and pay the car off…any advice?

#2

They probably don’t want to give you any exact numbers until you make the payment because it depends on when the payment is made.

If they give you exact numbers and then you don’t make the payment for another month the amounts might change slightly due to interest.

Here are a couple of online amortization sites to help you get some ball park numbers.
http://ray.met.fsu.edu/~bret/amortize.html
http://carpoint.msn.com/finance_insurance/main.asp

Generally speaking, your payments stay the same when you pay off a large portion of loan. I would think that the interest percentage should go down though. You would be paying 17.9% interest on a smaller about of principle. Maybe car loans work differently, I don’t know. I would suggest calling back and talking to someone else. Maybe the girl your wife talked to didn’t know what she was talking about.

#3

I’m not quite clear on what you’re asking, but you seem to be talking about two different things.

If your loan actually is amortized by the bank, the p/i portions of each payment are already scheduled; the amount of interest you pay each month should not be changed by a large payment, at least as long as principal remains. This sounds like what the bank said.

Most car loans are not amortized, however, so a large payment should reduce the interest portion of later payments. This sounds like what you were saying. Setting up a spreadsheet to approximate the results is not difficult.

Note that in both instances the amount of the monthly payment remains the same; that is determined by the loan agreement- a contract that can only be changed by another contract; i.e., refinancing.

Also note the bank won’t make any projections until they have the money in hand. They don’t want to say something and have it come back because you (not you, personally, natch, but “you” the customer) didn’t understand; nor do they want to take their time to explain things that are only theoretical.

#4

In terms of paying off a car loan, you basically have two options:[ol]
[li]You can apply the money directly to the principle. This is the smart thing to do as it will save you money on the interest, alot if the loan has long to go. But your next payment will still be due the coming month (although there will be fewer payments left.)[/li]
[li]You can use the money to pre-pay loan payments for as long as you can (the money divided by the monthly payment equals the number of pre-paid payments). This is not really the smart thing to do as you’re just buying time. Your next payment won’t be due for awhile but you’re not saving any money on interest because you’re not shortening the term of the loan.[/li][/ol]
Doing anything else involves refinancing, which may not be worth it with just a car loan.

#5

If any lump-sum payments you make later on will go directly towards paying off the principle on the loan, then your effective interest rate will decrease. Plugging a $17,000 loan at 17.9% interest over 5 years into the financial calculator I have gives a monthly payment of $431 for the 60 months. (a $450 payment = 20% interest; I’m guessing that they’re pocketing $19/month as some sort of expense to them…? Rounding the figure to the nearest $50? Something I’m missing?). Assuming that the first payment is due at the end of January 2001, by June 2001, you will have made a $913 dent in your principle payments, with the rest of your five payments going to interest. So to pay off the loan, you’ll have to cut a $16,087 check (actually $16,087 + 243 for June’s interest payment).

If you partially pay off the loan, your monthly loan payments will not decrease afterwards. However, a greater portion of your monthly payment will go towards paying off the principle. This is because loans are structured so that earlier payments consist primarily of interest payments whereas later payments consist mostly of principle payments. By partially paying off the loan, you will be paying less interest overall, and of course, you’ll pay off the car sooner.

To use your example, if you paid $10,000 in June, you would have a principle balance of $5,955 left. The car would be paid off by October 2002. Over the life of the loan, you will have only paid $2230 in interest, rather than $8,860 as if you had kept the loan for the full five years and simply made the monthly payments.

(Note: I’ve used the 17,000 loan @ 17.9% APR for 5 years figures I have, amounting to $431 / month. Your numbers will differ somewhat, but the idea will be the same).

#6

I guess I’m pretty naive when it comes to improving your credit rating. Why would it fail to improve your credit rating if you paid off your loan 4.5 years early? Isn’t that a GOOD thing? Shows that you give the banks their money back toot sweet?

#7

The answers to your questions depend on what kind of loan you have and the policies of the lender.

The prepayment question(s) cannot be anwered as stated because the interest calculation method is not disclosed. The most common method for a car loan is simple interest. The formula for determining the cost of a simple interest loan is P(rinciple) x R(ate %) x T(erm in years). There may or may not be a prepayment penalty on a simple interest loan, check your contract.

The other fairly common interest calculation method for car loans is the “rule of 78” AKA “sum of digits”. This method is MUCH less consumer friendly. Interest is calculated the same as simple interest, but is front loaded into the payments. The name comes from the fact that the sum of the number of months in a 1 year loan is 78 (1+2+3…+12=78). In the first month you pay 12/78 of the total interest, in the second month 11/78, etc. The final payment is 1/78 interest and 77/78 principle. Paying off a 1 year sum of digits loan after 6 months means you already paid 57/78 (73%) of the total interest, as opposed to 50% with a simple interest loan. It’s a kind of built-in prepayment penalty. Multi year loans use the same idea, just change the denominator (sum of digits for 2 years = 300 denominator instead of 78). Sum of digits is illegal in some states.

As to whether an over payment one month will affect the payment due in subsequent months, that is up to the lender. In most cases the payment will remain the same but I did have one car loan that deducted any over payment from the subsequent amount due.

#8

Credit reports (or at least all I’ve seen) show a loan’s current balance, highest balance, date paid off, and the month the loan was first reported. In addition, it lists whether a payment was on time, 1, 2, or 3+ months late for each of the last 24 payments, and the total number of late payments in each of those categories.

So, paying it off early wouldn’t show up. Yes, you made 6 payments and then paid it off, but who’s to say it wasn’t a 6-month loan?

IMHO, a creditor would rather deal with someone who has a longer, consistent history than someone who only borrows short-term.

But, then, IANAL; YMMV.

#9

My vote would be to pay off the car entirely in June and not worry about your credit rating. This is assuming all you pay is principal and no “advance” interest payments such as for the rule of 78. Go back and read your loan contract carefully to see how your payments are structured. At 17.9% (ouch!) interest you could end up paying several hundred dollars to “improve your credit rating”. How much is this worth to you? Why do you need to improve it?

If you decide to keep the car loan and these were incentive stock options you might consider holding some shares for a year to get long-term capital gains treatment and pay less income tax. Don’t hold too many or you’ll get caught by the alternative minimum tax. On the other hand, the way the stock market has been going, you may want to sell them as fast as you can.

#10

If you are conversant with Lotus123, just make your own amortization table and you can plug in any principal payments you want to tell you when the loan would be paid. The interest on a consumer loan is calculated ahead of time and then added to the principal; then it’s divided up into equal payments for convenience. That’s why the payment is almost all interest in the beginning. I don’t believe the rule of 78’s is allowed anymore, at least in federally-charted banks. Every month the amount of the payment that goes to principal increases, and the amount to interest decreases, so you need the table to tell you the proportions. I think you may have misunderstood the bank. The interest rate remains the same, but of course the balance it is calculated on changes whenever you make a payment, or an additional principal payment. The bank can’t tell you because customer service probably just uses a computer to tell them current information. There may be an amortization schedule in your loan file, but I doubt it. I make a schedule whenever I get a loan for this very reason, so I can see the effect of early principal payments.

#11

Sorry this took so long, forgot about this thread until it sank.

What was conveyed to my wife was that after a partial payment was made, we would still be making the same payment, which would still be 60/40 principal/interest. This didn’t seem right to me. I didn’t expect the payment to go down unless we somehow refinanced it, but I thought the percentage that was applied towards the principal would increase greatly.

The car cost somewhat more than $17,000, but less than $18,000. I was pretty sure we got 17.9%, but I might be wrong if it doesn’t add up. The payment is $447 I believe.

#12

60 monthly payments of $447 at 17.9% APR gives an initial capital of $18150.

The correct notation doesn’t transcribe very well, but basically 17.9% pa is the same as 1.38168% per month - and an annuity certain lasting 60 months at this rate is 40.61[sup]a[/sup]. 40.61 x 447 = 18150.

Implied APR for 60 payments of $447 giving initial capital of $17,500 is 19.9% pa

Before answering the rest of the question, a little notation.

a[sub]n[/sub] means a series of payments of 1 for n time units (in this case months). Without going into the maths, the value of this is

(1 - v[sup] n[/sup]) / i

where i is the rate of interest (19.9% pa which is 1.5239% per month) and v = 1 / (1 + i)

You can work out how much of the payment is capital and how much is interest by noting that immediately before the nth payment you had to pay

447 x a[sub]60-(n-1)|[/sub]

whilst immediately after you had to pay

447 x a[sub]60-n|[/sub]

this means that with the n[sup]th[/sup] payment you pay off capital worth

447 x (a[sub]60-(n-1)|[/sub] - a[sub]60-n|[/sub]) = 447 x (v [sup]60 - n - 1[/sup] - v [sup]60 - n[/sup]) / i

The rest of the payment (447 - this) is interest.

The interest portion of the payment does reduce over time. If you pay back some of the capital then a few things could happen[list=1][li]Loan is restructured with same term. In this case the 447 will be reduced as if you are taking out a brand new loan with a term equal to that currently remaining. The bank probably won’t want to do this for a loan of small term (i.e. yours).[/li][li]Payments continue as before but with new shorter term. In this case the situation is just like you’ve been transported to a point much nearer the end of the loan.[/li][li]Hi Opal.[/list=1]The latter is more likely. In this case, note that the proportion of the payments that is interest has dropped substantially (you are nearer the end of the loan).[/li]
Hope this helps.

pan
[sup]a/sup/0.0138168, for those who care

#13

Example:

PV = 18000
i = 17.9
n = 60 months
PMT = 447.00

A = 18000

B=Payment… C=Interest… D=Principal… E=Balance

447 (30 day mo.)… ((A*(.179/36530))… (B-C)… (A-D)
447 (31 day mo.)… ((A(.179/365*31))… (B-C)… (A-D)

To get a close approximation, you can just use .179/12. In Lotus123 just copy down the page the equations for each month, and it automatically changes the cell numbers. If you want to know what effect a principal payment will have, once you have the regular schedule finished, just substitute the amount you plan to pay for D and it will recalculate the term of the loan.

#14

amortization aside…

the best thing to do, IMHO, would be to pay off the car all together, then use whatever $$$ you have left over to get a secured credit card. Best of all worlds - car’s paid off, and you’re rebuilding your credit.