Car Loan Rates

Date: 08/27/97 at 11:55:45
From: Tina Fulton
Subject: Help with car purchase

Dear Dr. Math,

I need to buy a car and wondered if you could find the time to help me 
figure something. Please show me how to calculate the impact of 
different interest rates on a 5 yr. loan (60 payments) of $20,000.

My credit union will loan me that amount at 8.4 percent, and they 
estimate payments of about $400 a month. The salesman at the 
dealership is putting heat on me to use their loan service, which 
can give me the loan at 8.0 percent, possibly less. So my question is: 
how much would I save over the next 5 years if I take the car 
dealership loan at 8 percent or at 7 1/2 percent?  Does it make 
sense to try to whittle them down $300 or $400 on the price of the car 
and then stay with my credit union loan, or would I gain substantially 
by getting the $20,000 loan financed for 1/2 percent or even 1 percent 
less?  

I would appreciate it if you could supply me with actual figures. I'm 
sorry if this is confusing, but I only purchase a new car about 
once every decade and I'm a rookie at this.

Thanks,

Tina Fulton

Date: 08/27/97 at 13:23:17
From: Doctor Ceeks
Subject: Re: Help with car purchase

Hi,

Before answering, you must understand that Ask Dr. Math is not
responsible for any consequences of any decisions you make based
on the information in our responses.

We are not offering you any advice, but can treat this problem in
the abstract as a math question involving interest rates.

There is already a nice derivation of relevant information in
Doctor Anthony's response to a related question at the site; please 
take a look at it:

http://mathforum.org/dr.math/problems/chevellemn.7.4.96.html   

In your case, I compute the following monthly payments:

   At 8.4 percent: $409.37
   At 8.0 percent: $405.53
   At 7.5 percent: $400.76

   ($20,000 loan with monthly installments over 5 years)

The savings between 8.4 percent and 8.0 percent are about $230, and 
the savings between 8.0 percent and 7.5 percent are about $286.

I've tried to be accurate, but please double-check the arithmetic
for yourself.

-Doctor Ceeks,  The Math Forum
 Check out our web site!  http://mathforum.org/dr.math/