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This is a tricky question so please read through the
entire answer. It's this type of "fuzzy math" that can end
up costing people a bundle!
QUESTION: Which loan is better and why?
Loan 1: $100,000.00, 30-year
loan, with monthly payments of $665.31. That's a total out-of-pocket
cost of $665.31 x 360 months = $239,511.60.
Loan 2: $100,000.00, 15-year
loan, with monthly payments of $1,014.27. That's a total
out-of-pocket cost of $1,014.27 x 180 months = $182,568.60
ANSWER: Loan 1 is better
because it really does cost less!
Let's pretend that I already have
loan 1. Now imagine having a mortgage broker trying to sell me loan
2 to replace my loan 1.
Here's the pitch. "Scott,
listen, if you do a 15-year mortgage with the $1,014.27 monthly
payment, you'll save $56,943.00! Just sign here!"
 Is the broker lying? Well, not
technically, however it is true that loan 2, even though it
"seems" like it saves you money, is actually more
expensive!
Even under the sales pressure I would
go get my calculator to figure out the most important cost for
any loan, the interest rate (APR).
It turns out that Loan 1 is 7% and
Loan 2 is 9%. I used the DebtSmart Loan Calculator to get the rates.
Use this link to find out how you can get the calculator: http://www.debtsmart.com/offers/p_debtsmart_calc.html
Armed with that information, I'd say
to the mortgage broker, "Why would I want to use the 15-year,
9% loan over the 7% loan?" To which the response is, "Rate
doesn't matter, you save $56,943.00! Scott, are you trying to tell me
that you don't save $56,943.00, are you saying that I'm a liar!"
He's not lying. It's true that loan 2
does save $56,943.00 over loan 1.
So then, how is it better to use loan
1? How can loan 1 possibly be cheaper when it is true that loan 2
saves $56,943.00?
Fuzzy math!
It's an unfair math comparison. A
trick question. It's not an apples-to-apples comparison because the
monthly payments are not equal!
I would say to the broker. "Rate
does matter. If I can afford to make a $1,014.27 monthly payment to
loan 2 then I can afford to make the same payment to loan 1. When I
do that I can pay off loan 1 in 12.27 years. Which is obviously much
shorted than the 15-year option. In fact, if I did that I can pay
off loan 1 with a total of $149,341.11. That pay off figure is
$33,227.49 cheaper than the 15-year option!"
At that point the mortgage broker
would either act confused, because he doesn't get it, or look
surprised that you figured out his fuzzy-math game.
The main key to comparing loans is being sure that the comparison is fair. That means that you can
only have one parameter change and all others held constant. To make
a fair comparison in this case the principal ($100,000) and
payments must remain the same for both situations. The change is in
the rate (7% or 9%). Keep in mind that the repayment-times change
however, it's because the repayment-time is a function of the principal, rate,
and payment.
Once we make the fair comparison, it's
clear that loan 1 is the better, cheaper loan.
Quick mention...many people did
respond and say that loan 1 was better because you can use the
difference between the payment for investment purposes.
Of course,
you need to know the interest rates before doing the investing since
to make the investment worthwhile you'd need to make the same rate
as the loan cost just to break even. However, thinking about
"using the difference between the payments" is a clear
sign that there's extra money floating around. That extra money is a
symptom of the "fuzzy math".
--End--
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