Monthly Payment Help

finitehelp · 2012-02-23 17:27:28

Hi,

I'm having trouble understanding the Monthly payment formula such as (P x (i / 12)) / (1 - (1 + i / 12)-n).

For example, when I try to calculate the monthly p on a 25,000 loan, with a 6% interest rate and a term of 36 months. I multiply 25,000 x 0.005 which gives 125. Then, I add 1 + 0.005 = 1.005 and raise that to -36 power, which gives 0.84. Then I subtract 1 and that gives -0.16. Then I divide 125 by the -0.16 and the answer comes to -781.25.

I know that the answer should be 760.55, so what am I doing wrong?

Please break it down completely and provide each step with this example. Also, please provide some other examples with different loan amounts, interest rates, and months so I can understand better.

Thanks!

bobbym · 2012-02-23 19:47:06

Hi finitehelp;

(P x (i / 12)) / (1 - (1 + i / 12)-n)

First, the above formula is incorrect.

It should look like this:

Do the numerator first,

Now work on the denominator by doing the innermost parentheses first.

Again do what is inside the parentheses first,

Now dvide 125 by .164355081

760.55 when rounded.

phrontister · 2012-02-24 03:02:28

Hi finitehelp,

(P x (i / 12)) / (1 - (1 + i / 12)-n)

The only error I see in your formula is that 'n' isn't a power, although in your workings it is.

The formula should be (P x (i / 12)) / (1 - (1 + i / 12)^-n)...but bobbym's LaTeX version is much clearer.

Then I subtract 1...

That is incorrect. 1.005^-36 should be subtracted from 1, not the other way around. That error resulted in your answer being a negative number.

...which gives 0.84......and that gives -0.16

Rounding (1 + i / 12)^-n to only two decimal places and maintaining that number of decimal places for the subtraction from 1 gives 781.25, instead of the 760.55 (rounded) that you get by going to more than 8 decimal places .

Last edited by phrontister (2012-02-24 04:41:00)

finitehelp · 2012-02-24 05:14:30

Thanks so much this was the best explanation. Thank you both

bobbym · 2012-02-24 06:57:39

H finitehelp;

You are welcome!

Hello phrontister!

phrontister · 2012-02-24 10:53:56

G'day, Bobby.

I thought I'd join in here and add to your post by answering the question along the lines of identifying and correcting the errors in the OP's original calcs.

LaTeX is so good for presentation clarity, and helps with spotting errors like these.

bobbym · 2012-02-24 11:24:22

Hi phrontister;

Glad to have you. The more the merrier!

The latex is the key. I had a teacher who said to me, " I know you know the work but after grading 200 papers and then coming to your mess, I just give up." My first reaction was to punch her but when I looked at my work, I could not read it either. My notes looked like a squirrel with wet ink on his feet had done the rumba across my sheets. So I punched myself instead. Half of doing anything well is doing it neatly.

I just thought I would mention that to you youngsters ( 27 year olds ).

phrontister · 2012-02-24 21:19:11

Hi Bobby,

Thanks...I'm always happy to learn from my elders.

So I punched myself instead. Half of doing anything well is doing it neatly.

I hope you punched yourself very neatly...but having seen a photo or two that you posted of yourself I'm not so sure you managed to do that.

bobbym · 2012-02-24 22:41:06

Yes, it was a neat punch to the lower abdomen.

Thanks...I'm always happy to learn from my elders.

Young people!

Math Is Fun Forum

#1 2012-02-23 17:27:28

Monthly Payment Help

#2 2012-02-23 19:47:06

Re: Monthly Payment Help

#3 2012-02-24 03:02:28

Re: Monthly Payment Help

#4 2012-02-24 05:14:30

Re: Monthly Payment Help

#5 2012-02-24 06:57:39

Re: Monthly Payment Help

#6 2012-02-24 10:53:56

Re: Monthly Payment Help

#7 2012-02-24 11:24:22

Re: Monthly Payment Help

#8 2012-02-24 21:19:11

Re: Monthly Payment Help

#9 2012-02-24 22:41:06

Re: Monthly Payment Help

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