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.0232842787

A

archcommus

Diamond Member
P(t) = P ( 1 + r / n ) ^ (nt)

Standard equation for calculating total amount paid on money borrowed or invested. n of course is the period, i.e. 1 for compounded annually, 4 for quarterly, 12 for monthly, etc. The number in the title of my thread, .0232842787, is the number for n which makes this equation work properly for car payments.

Now tell me, what the heck is the significance of this number for calculating car payments? Technically, this should have some relevance as to how often they compound the interest, but it doesn't seem to.
 
No idea. I tried plugging into a decimal to fraction converter and I didn't get very far.

AFA the fraction is concerned, the number is close to 1/43, but much closer to 4889/209970 and 51325/2204227

Text
 
Well the fraction equivalent doesn't really matter. All I know is that you can't use the standard interest equation to calculate total paid for a car loan, witha typical n value of 4, 12, or 1. However, if you use my big decimal for n, it comes out pretty much correctly. So my big decimal is technically the amount of times per year that car loan interest is compounded. But that makes no sense.
 
It has no significance because it's the unique solution that makes your formula produce the same result as the correct general formula which is Prt / (1 - ( 1 + r / n ) ^ (-tn))
 
Originally posted by: b0mbrman
It has no significance because it's the unique solution that makes your formula produce the same result as the correct general formula which is Prt / (1 - ( 1 + r / n ) ^ (-tn))
Click to expand...
That is probably right. But can you tell me how that equation is different from [P(1+r/n)^nt] all divided by nt to get a monthly payment?

 
Your search - .0232842787 - did not match any documents.

too bad the goggles don't work.

(maybe ask someone at a math forum? this is OT chat... aka "not much thinking involved" chat) 😛
 
I understand that the number probably has no meaning. My question is, why can you not take the standard equation to figure out total amount owed on a loan after t years, A(1+r/n)^(nt), and then divde that by the number of months to get a monthly payment? That gives you the wrong answer, whereas the equation b0mberman posted gives you the right answer.
 
P = the beginning amount of money
r = your interest rate
n = the frequency of interest (quarterly, annualy, monthly, etc)
t = the total length of time of this equation

The .0232842787 number you have has no significant value towards holding a constant in this equation.

Please ask me anything else as I love math!!!

Also, check out http://www.physicsforums.com for more cool stuff! 🙂
 
Originally posted by: jamesbond007
P = the beginning amount of money
r = your interest rate
n = the frequency of interest (quarterly, annualy, monthly, etc)
t = the total length of time of this equation

The .0232842787 number you have has no significant value towards holding a constant in this equation.

Please ask me anything else as I love math!!!

Also, check out http://www.physicsforums.com for more cool stuff! 🙂
Click to expand...
Yes, we have already covered that. Refer to my post two posts above yours.
 
Originally posted by: archcommus
I understand that the number probably has no meaning.
Click to expand...


Where I come from, 'probably' equates to uncertainty. 🙂 I was confirming your doubts with a positive answer.

You can solve that equation to figure out a loan after t years, assuming you have enough numbers and the right ones, too. 😛 Give us your numbers and let's see what we get.
 
Originally posted by: jamesbond007
Originally posted by: archcommus
I understand that the number probably has no meaning.
Click to expand...


Where I come from, 'probably' equates to uncertainty. 🙂 I was confirming your doubts with a positive answer.

You can solve that equation to figure out a loan after t years, assuming you have enough numbers and the right ones, too. 😛 Give us your numbers and let's see what we get.
Click to expand...
Yes, thank you for the confirmation. :thumbsup:

I was just playing around with the numbers. Let's make up an example. $16,000 loan at 6% interest for 60 months. I figured, I should be able to use P(1+r/n)^nt to figure out how much total is paid back, and then divide that by 60 to get monthly payments. However, that actually gives you payments of about $50 more than what they really are, if you use the proper equation that b0mberman posted. So why is the first method wrong?
 
Originally posted by: archcommus
So why is the first method wrong?
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Compound interest.

If you use p*(1+r/n)^nt, you assume that no payments are being made. At your numbers ($16,000 and 6% interest), that means after the first month, you owe $80 interest. Thus after one month, you owe $16,080. Next month you owe $80.40 interest. Why 40 cents more? Since you didn't make a payment, you owe interest on the interest. By the 60th month you owe $107.37 in interest since that interest kept building. The total amount you now owe is $21581.60.

If you make payments on a car loan, the total amount you owe drops each month. Thus the amount of interest you owe drops each month. If you made a payment of $309.32, then add in the $80 in interest, you owe $15,770.68. Next month you only owe $78.85 in interest. Notice how the interest is lower in this case since you owe less on the second month? The interest keeps dropping each month. On the 60th month, you only must pay $1.54 interest, and your final balance is 34 cents. (Your last payment will be slightly off since we don't have partial pennies anymore).

The two cases are completely different.
 
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