# A quick question on loan interest

Real quick-I’m 27 and mathematically inept, but this question is NOT homework, so please don’t shy away from answering it on that basis.

Okay, I refinanced my Jeep today, dropping my interest rate to 4.99%. The new borrowed amount is \$16,663.79, and it’s a 48 month note. The interest rate is fixed. In addition, I had to add \$65 because of the title transfer fee.

So I figured the payments like so:

16663.79 + 65=16728.79

16728.79 x 1.0499=17563.56

17563.56 / 48 = 365.91

Can anyone explain how the payments are coming out to \$383.20?

Your calculation assumes that the total amount of interest you’ll be paying, over four years, is 4.99% of the total loan amount. However, it’s actually one-twelfth of 4.99% of the outstanding loan balance per month, for 48 months. If you’ve got Excel, check out the PMT function. Someone with a better memory than mine will probably be along shortly to give you the proper formula for figuring out the monthly payment on a loan.

Here’s the formula:

pmt * [1 - (1 + i/p)[sup]-N[/sup]]
----------------------------- = PV
i/p

so we have:

pmt * [1 - (1 + .0499/12)[sup]-48[/sup]]
----------------------------- = 16728.79
.0499/12

This gives me payments of \$385.18. I’m not sure why your payments are \$383.20, but it looks to me like you’re getting off a little cheap, actually.

Here’s a site that shows you how to do the computation, if you don’t have Excel. It’s basically the same for a car loan as it is for a mortgage. In the example they give, they do a quarterly payment, whereas you’ll need to compute it for a monthly payment (i.e., divide 4.99% by 12 to get the monthly interest rate, etc.).

I suppose the periodic interest payments on some loans are still figured using something called the Rule of 78s, but that’s another kettle of fish.

I’ve seen this, before, Cabbage, and I think it has to do with the way banks handle fractions of pennies. I believe that, at some stage of the computation, they truncate, rather than rounding, so they end up shorting themselves a bit on the total interest. The Excel function, BTW, also gives \$385.18, so your arithmetic is impeccable!

Something else you need to consider is whether the 4.99% is the APR or your “quoted” interest rate. Those guys give you your interest rate WITHOUT figuring in any other costs - processing fees, credit report charge, orig. fee - whatever they have - all these increase your loan amount, which is what your APR is figured on. The APR is the ONLY figure that matters - any other rate they quote you is “sale-speak.”

The payment quoted seems to be based upon paying rather than financing the \$65 fee. I get \$383.70 rather than \$383.20, but close enough for banking work.

My guess is that the interest rate is something like 4.93%, but when they quote the APR, they have to indicate a higher rate which accounts for the various fees you have to pay. Look at your paperwork and find the true rate to do the calculations with.

BTW, your method of calculation was wrong for two reasons:

1. The 4.99% is an annual rate, and you’re trying to use it to calculate a monthly payment, and
2. if you did it that way, you’d only be paying the interest, and you’d never pay off the principal.

Well, even though I didn’t get the answer I wanted, I thank you all for your responses.

I guess it just seemed odd that I went from payments of \$398.20 at 10.75% for 72 months to \$384.70 at 4.99% for 48 months and only saw a drop of, what, \$13.50? (The loan officer told me the \$65 would add \$1.50/month on the payments.) But it’s right there on paper, so I’ll just suck it up.

It’s the shortened loan length that did that. Look at your savings over the life of the loans-you might be surprised. If you’ve been paying the old rate for less than two years, then you can’t just compare the payments, because you’re paying it off faster …

Not knowing your exact circumstances, I’ll suppose that you’ve been paying on the Jeep for 12 months at the higher rate. Your total payments over the 72 months would have been \$28,670.40. Instead, you paid at that higher rate for 12 months (\$4778.40), then at the lower rate for another 48 months (\$18,465.60), for total payments of \$23,244.00 over the life of the loan. You’ve saved \$5426.40 in payments with your refinancing, and the car is all yours a year earlier. I’d buy that for a dollar!

My math skills atrophied shortly after high school. Can someone point me toward an online calculator that will show me how much of each payment I make is interest and how much is principle. If it can handle showing me how much sooner my note is paid off with extra principle payments, so much the better.

Flypsyde

I’ll try and sum this up for you. Most loans, mort./auto/credit cards, etc… charge you interest on a daily basis. Int rate/# days in year. So you are being charged interest on your principal balance daily. You send in your payment, the first portion of your payment pays off the interest that has been charged to you over the last 30 days, the remaining goes to the prinicipal. Now, your principal in slighgtly lower. So, when they charge you interest daily it is a slightly lower amount because the prin. has gone down. When you send in your next payment the amount of int. for the month is slightly lower, so a little more goes toward the principal. The formulas you have seen just calculate what amount paid every month will make that last payment take the princ. to \$0

Otto

If you email me I have a spread sheet set up that calculated just what you are looking for.

Here are a bunch of financial calculators
http://www.savingsinstitute.com/Pages/Financialcalc.htm