Date: Sun, 8 Apr 2007 08:51:45 -0500
From: BreadWithSpam@fractious.net
Newsgroups: misc.invest.financial-plan
Subject: Re: What to pay off first--student loan vs. car loan
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"Daniel T." writes:
> joetaxpayer wrote:
> > Daniel T. wrote:
> > > Let's say you can put an extra $1,000 over and above the minimum
> > > payments on one of the loans to help pay it off. Which would save
> > > you the most money? Well if you put the thousand on the car loan,
> > > you will save $54.90 times the number of years left on the loan.
> > > If you put the thousand on the student loan you will save $38.75
> > > times the number of years left on it. So how many years are left
> > > on each?
> >
> > That logic will produce flawed results.
>
> Why? I'm just learning here. It seems to me that if putting a $1,000 on
> one loan would save me $275 (assuming loan 1 is 5 years) and putting a
> $1,000 on the other would save me $387 (assuming loan 2 is 10 years)
> then I should put the money on the one that saves me the most...
I know it *looks* like by multiplying by the number of years
remaining, you are taking time-value of money into account,
but you are not. In order for it to (better, but not perfectly)
do so, you need the same time periods. Look at it this way:
Let's look at two debts and I'm going to make up some easier
number - suppose you have a 5 yr loan at 5% and a 10 yr loan
at 3%. The sizes of the loans isn't important for the moment,
but we're going to assume you have $1000 in hand available
to pay one of them down. According to your method, paying
that $1000 on the 5yr loan will save you $50/yr for 5 yrs = $250
and on the 10 yr loan, it'd be $30/yr for 10 yrs = $300.
The thing you're ignoring is that second 5 years - by paying
down the 10 yr loan, not only are you not paying the $150
in interest in the first 5 years, but you are not paying
the $150 in interest during the second 5 years. With the
5 yr loan, you are not paying $250 during those first 5
years, but your *also* not paying any interest during those
second 5 years *either*. You cannot ignore that. So you
need to either assume that had you not paid off that first
loan, then after 5 years, you'd have had to refinance it
or borrow again and pay some interest - who knows what -
during that second 5 years. Or you have to ignore that
second five years for both the first and the second loan -
in which case, your choice isn't $250 for one or $300
for the other, but, indeed, saving $250 for one or $150
for the other.
In other words, if you compare interest over time, you need
to match the time periods one way or another. An interest
rate is a *rate* - an amount *per year*. So you have to
compare over the same number of years.
There may be other considerations (ie. cashflow, minimum
payments, liquidity, etc) but all else being equal, it's
generally going to benefit you more to pay off the highest
rate first, at least in simple dollar terms. Not the longest,
not the highest balance, but the highest rate.
> > It would suggest that a 30 yr loan at 4.5% should be repaid faster
> > than a 12% credit card that has a 5 year payback.
>
> That would depend on how much you owe on each.
It would not. A 12% credit card versus a 4.5% loan means you
are paying more interest over any identical time period. During
year on, $1000 loan at 12% means you are paying $120 to someone,
versus paying $45 to someone. At the end of year one, regardless
of the term remaining on the loan, you have less money if you pay
the higher rate.
There may be other considerations - generally cashflow-related
ones (ie. size of minimum payment, etc) - but in general, if
you want to keep more of your money, pay the highest rate loan
off first.
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