Understanding Car Loans

[SD]

I was doing calculations on my car loan and for some reason my numbers
don't match what I am paying or what shows up on kbb.

For e.g. My car loan is 60 month on $25185 at 3.9%

I pay 462.68/month which is the same as what kbb.com comes up with in
it's calcualtion. I understand this is a 3.9% simple interest loan.

My calcuations = 25185*1.039/60 come out to be only 436.12

What have I missed here?

Thanks
SD

[Rich Carreiro]

SD <siddhar...@COLDmail.com> writes:

You missed an understanding of how amortized loans work.

Try looking for a mortgage or consumer loan calculator
online and plug the 60 months, $25185, and 3.9% into
it. It'll spit out $462.80.

Here's what's going on...

You start with your initial balance B. You get charged monthly
interest r/12 on that balance. So at the end of the first month
your balance is
B + (r/12)*B = B(1 + r/12)

Then you make your monthly payment p. After that, your balance is
B(1 + r/12) - p

Next month the same thing happens. You are charged r/12 interest
on the balance, then have your payment subtracted off. So after
the 2nd month your balance is
B(1 + r/12)^2 - p(1 + r/12) - p

And after the 3rd month your balance is
B(1 + r/12)^3 - p(1 + r/12)^2 - p(1 + r/12) - p

and so on.

If you say "and after 60 months of making payments of p, the
balance is zero", you can grind the algebra and get a formula for
p in terms of B, r, and the number of months. Poke around a bit
with google and you should find the formula easily.

Your p = B(1 + r)/n formula says, in words "Apply a total (i.e. not
per year) interest rate of 3.9% to the principal and pay that combined
balance off evenly over n/12 years." The actual annual interest rate on such
a scheme is much less than 3.9%.

--
Rich Carreiro rlc...@animato.arlington.ma.us

[T R]

When in a bind.... Here is a way I like to approximate amortization of short
loans in my head or with a simple calculator. It's not exact, but it comes
pretty close for many kinds of loans. The approximation is that the
principal declines on a straight line, so the interest paid over the life of
the loan is half the interest on the initial principal (approximately).
This is since the average value of a straight line descending From x at
t=zero To zero at t=maturity is x/2. The approximation works out quite well
for short loans at low rates, such as auto loans. Not so good for a 30-yr
mortgage at 12.5%, where the amortization curve is a tad bit more
convex....:)

$25185 principal * .039 interest * 5 years * 0.5 approx factor = $2456

This is the approximate interst paid over the life of the loan.

Add to principal, and divide by the number of payments to come up with the
monthly payment:

($2456 + $25185) / 60 payments = $461

Not too far off ($462.80 is the exact answer), and pretty good if you are in
a bind. If you are good with numbers in your head, you could approximate
this math in your head. Pretty neat to close your eyes for 15 seconds and
amortize a loan in your head when at the dealership :)

T.

"Rich Carreiro" <rlc...@animato.arlington.ma.us> wrote in message
news:m3d5z5f...@animato.home.lan...

[SD]

>
> $25185 principal * .039 interest * 5 years * 0.5 approx factor = $2456
>

THanks, I figured this the moment I pressed the send button. I forgot
the 5 year part :)