# Car loan

(male narrator)
So suppose that you can…
that you can afford \$200 a month as a loan payment,
uh…on a car. Uh…if you
can get a loan for 3…at 3% interest
for 60 months–or 5 years– uh…how expensive of a car
can you afford? In other words, what amount loan can you pay off
with \$200 a month? Uh…so there’s
a few key words here. The biggest key word
is “loan.” The fact that this is a loan
tells us right away that we are looking
at a loan-type problem, uh…and loans have
their own type of equations. It turns out that this equation
is exactly the same as the one
for payout annuities. Uh…’cause really
just you and the bank are reversing roles, because now you–
the loan holder– are the one paying
the interest, rather than the bank
paying the interest. So the equation
is the same– P0, uh…equals d times 1,
minus 1, plus r, over K, to the negative K, times N,
all over r, over K, where in this case, d is the loan payment…
each month, or year, or whatever the frequency
of the loan is. So let’s break this down. We wanna know… oh, sorry, and P0 is
the, uh…initial loan amount. Loan amount…there we go. So…what is the initial
loan amount in this case? Well, we don’t know, right? That’s what
we’re looking for is how much of a loan
can we afford. So we don’t know P0 here. What we do know is what we
want the loan payments to be. We want the loan payments
to be \$200. We know
that the interest rate that we can…that we…
we’re gonna get is 3%. We’re talking
about monthly payments, so K is gonna be 12–
12 months in a year– 12 times 5 years…
notice that 12 times 5 isn’t… is those 60 months,
over .03, over 12. Uh…and this
is gonna give me the…uh… and this is the equation
I need to evaluate in order to figure out,
uh…what my loan is… what kind of loan
I can afford. So I could go ahead
and evaluate .03 over 12 is… is .0025, uh…negative 12
times 5 is negative 60, uh…and this is .0025. Uh…and so now I just need
to evaluate this to figure out
the amount of my loan. And I’m gonna skip
the calculator this time. And it turns out
that the answer is 11,100… oops, one too many values
there…uh…\$11,120 loan. So that’s how much loan
I can afford. Now you might be wondering
how much interest am I gonna pay over the life
of this loan? In other words, how much
is this credit going to cost me? Uh…so to figure that out, we can go back to the idea
of how much did I pay, uh…versus how much
was the loan? So how much
would I pay? How much do I pay? So let’s think about that. I pay \$200 each month
for 60 months. Right, 5 years times 12
is 60 months. I pay a total of \$12,000
to the loan company. How much of that
was the principle or the original amount
of the loan? Well, the original amount
of the loan was \$11,120, presumably, which means…\$880 of this loan
is…interest. So in other words, I’m paying–
over the 5 years–\$880, uh…to the loan company
for their service– for them offering me
this credit.