(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.

So I just worked out this problem using your formula and not skipping the calculator and I came up with $11,130.47154. Did I do it wrong or is your's a miscalculation?

+Lori D it's probably a rounding error when calculating. (Tfw u probably don't care about this section anymore XD)