# Clever math, clever reasoning

by coberly

Math and Math

I was looking at a book called “The Standard and Poor’s guide for the
New Investor,” by Nilus Mattive.

In it I found offered the following counterintuitive argument (page 9):

Suppose you inherit 40,000 dollars and you want to buy a 40,000
dollar car. You can get the car for no money down at 5% over 48
months., while putting the 40,000 into a bank account at 4%. Or you
can pay cash. Which should you do?

The author says put the money in the bank and pay for the car on time.

Then he shows how the 921 dollar monthly payments add up to only
\$4,216 in interest over 48 months, while the bank pays \$6,794 on the
40,000 over that time. (\$6,920 if compounded monthly.)

He explains this unexpected result is because the principal on the
car is being paid down all the time, so the interest payments are
smaller than you expected. And then he says this is why you need to
do the math.

I’d like to leave this as a problem for the readers of Angry Bear…

is Mattive right?

What he left out is that if you paid cash, you’d have those 921
dollar monthly payments to do with whatever you wanted. And if you
wanted to put them in the bank at that 4% interest, you’d have \$47974
in the bank at the end of 48 months instead of the \$46920 you’d have
had by leaving the \$40000 in the bank and making the car payments.

This is a fairly simple case of an expert dazzling himself with his
own cleverness. And the moral of the story is that it happens all
the time. Correct math, even clever math, is no guarantee that you
are making any sense. And that’s just the easy bits. He doesn’t
consider what you could be doing with that 40,000 instead of leaving
it in the bank, or with your time if you didn’t have to meet those
car payments every month.

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This one by coberly