Car Loan Question

This is very random but I was figuring out how car payments and loans work exactly and I understand everything pretty well now except for one part: how do they come up with the number for the initial payment?

For example, in this link, where did they get the $362.68? How did they arrive at that number?
http://www.theautoevaluator.net/resources.html

I now understand how interest rates work, how you pay less interest as your principle decreases, etc. I just want to FULLY understand the process and it's annoying the crap out of me that I can't figure it out.

The prize for whoever can explain (and get me to understand it) will be a hand written thank you note and stickers, should you wish to accept it.

-Mike

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in an effort to get the prize, im just going to post this and hope it's right

calculate a loan payment or amortization schedule manually if you like running the numbers yourself or want to verify the accuracy of an online loan calculator.

The formula is M = P * ( J / (1 - (1 + J)^ -N)).
M: monthly payment
P: principal or amount of loan
J: monthly interest; annual interest divided by 100, then divided by 12.
N: number of months of amortization, determined by length in years of loan.

2
Follow the following steps:
3
Calculate 1+J. M = P * ( J / (1 - (1 + J)^ -N))
4
Take that to minus N power. M = P * ( J / (1 - (1 + J)^ -N))
5
Subtract answer from 1. M = P * ( J / (1 - (1 + J)^ -N))
6
Divide the monthly interest (J) by this number. M = P * ( J / (1 - (1 + J)^ -N))
7
Multiply the result by the principal or amount of loan. P * ( J / (1 - (1 + J)^ -N))

ok verified it working

362.68 = 15K * ( .00625 / (1 - (1 + .00625)^ -48))

but the worded answer would be thats the magic number where after 48 months of your principal balance payments that keep going up and interest payments go down, finally make the balance hit zero.

or the even sorter answer could be: fancy math crap

I'll take my hand written thank you in the form of a thank you forum post, if I satisfied the requirements.

Yea.... Um... Nope... Still makes no sense (that part at least). I think "fancy math crap" is the answer I'm looking for now tho after reading all that. I guess I understand most of the whole process, so that's good enough? Lol.

If you'd like your prize, Pm me your address. I'm a man of my word and am happy to oblige! :)

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lemme take another shot. When you pay the 362.68, you are making two payments. One payment goes toward the principal, which is what you actually owe on the car. The other payment is interest, which goes directly into the banker's pocket. The loan is designed so you pay more interest in the beginning, so they get as much money as possible. The above formula gives the loan company the magic number for them to make it happen, with a balance of zero at the end.

Every month you pay interest on the principal. First month you pay it on the full 15k, so ($15,000 * 7.5%) / 12 = $93.75, so your first payment will be 93.75 in interest. that is the loan company's profit.

subtract that from what you are paying monthly... $362.68 - $93.75 = $268.93. so that is the amount you actually pay on the principal. so now you only owe $14,731.07 ($15,000 - $268.93 = $14,731.07.)

2nd month you pay interest on the new principal, ($14,731.07 * 7.5%) / 12 = $92.07, subtract from the monthly payment $362.68 - $92.07 = $270.61, so now $270.61 is subtracted from the principal.

If you did this for 48 months, your principal would end up being zero (technically it's probably going to be off by a few pennies). You would pay much less interest per month at the end of the loan. Everything that is confusing about this is because the interest and principal payment change every month, but both add up to the monthly payment.


If you end up paying extra at any given month, that amount is fully taken off the principal, which does two things for you, it reduces the length of the loan and it reduces the interest you pay for every month after that. For example, my car loan is over in june (zero % loan so no point in paying it early), once it is over, I plan on putting the amount of my car loan toward my house loan. the extra money + the extra I already pay per month will turn my 15 year loan into 9 year loan, and cut the interest I pay by many thousands of dollars. If my snake business ever starts booming :rolleyes:, I can pay it off even sooner and farther reduce the amount I pay in interest.

it's all just fancy math crap :)

I understood all that part. I just didn't get where the $362 came from. I guess it's just some random equation I won't quite ever understand lol.

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I always looked at it like this. way amount of the car plus what they can get you for .over the time period of the loan ( my case was 5 or 6 years ) I am paying about 5k in interest. so my truck was a 10k truck and I paying about 5 k in interest, so they figure
.

L*ir =a ( a*length of loan) = profit + l= lm lm /length of loan = cost ( plus some other fees )

L= asking amount
ir = interest rate
a= the interest rate profit (at a flat cost for a year)
length of loan self explaining
profit= amount of total profit they can make if you complete the loan payment
lm( total amount you will promise to pay back when it all over
cost = rough amount you pay minus other fees they try to get you for )
so in this case

10k *.089= 890 ( 890* 60months) = 5340 +10000= 1534/60= 255.66 ( the payments I make are a little more as they charge some stupid fees ( extra profit )

more less they want to get as much of the profit up front so that why you pay more on interest than principal I bet in long run your actually getting charged extra in interest on the unpaid principal ( this being why you have almost an extra payment ( or larger payment at the end)
that why if they take the vehicle or house they can still turn a profit off of you those first couple years.

Quote:

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Originally Posted by Mike41793

I understood all that part. I just didn't get where the $362 came from. I guess it's just some random equation I won't quite ever understand lol.

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not exactly random. it's just how you figure out exponential interest with a loan of this type.

also looking at it, they have unnecessary parentheses in this formula, it can also be:

M = P * J / (1 - (1 + J)^ -N).

P * J Factors in your interest with your principal
(1 - (1 + J)^ -N) This gives a number to factor in the length of the loan, since the interest rate exponentially decreases. add the interest to 100% since the value is based off the principal and interest, so in the example it would be 107.5%, factor in the length of the loan, remove the 100%. now the value is purely based on the interest and loan length.

better?

I guess I get it about as much as I ever will... The formulas did help clear it up some for me.

Thanks guys!

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Congrats to you. I tried to figure this out years ago and while I'm horrible at math it wasn't any help. I gave up. lol.