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•  » Struggling with calc of interest compounding monthly

## #1 2013-06-03 17:41:03

mezzlepop
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### Struggling with calc of interest compounding monthly

Hi,

This is my first time on this site.  Amazingly clear explanations but I'm embarrassed to say that I still can't work out the calculation below.  Not sure if I should post this in 'members only' area or in this area?  So I sent it to both.

I will certainly return to the site and definitely be thanking anyone kind enough to assist with an answer and workings

Thanks, Mezzlepop

\$200,000 loaned at 14% per annum "in arrears calculated and charged on monthly rests", for 5.5 years.

No repayments made.  Looking for total amount repayable at the end of 5.5 years.

## #2 2013-06-03 20:52:24

SteveB
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### Re: Struggling with calc of interest compounding monthly

Hi

I should point out the following things:
(1) I have not done interest calculations for ages.
(2) The conventions used in the USA may be different to the ones that I studied many years ago.
(3) There are some terms used in the question that I do not know what exactly they mean.

http://en.wikipedia.org/wiki/Compound_interest

Look at the bit about "monthly mortgage payments" for a mortgage loan calculation.
(I now realise that this will go into some unnecessary depth, but it may still be useful so I have left the link in.)

I am not sure whether this is the same system implied by the question.
I am not sure what "in arrears calculated and charged on monthly rests" in terms of the monthly iteration formula.
However the principal of it may be the same with a few adjustments.

(Actually I have re-read the question and I can now see that the problem is easier than I had thought.)

Last edited by SteveB (2013-06-03 22:24:43)

## #3 2013-06-03 21:51:00

bob bundy
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### Re: Struggling with calc of interest compounding monthly

hi mezzlepop

Welcome to the forum.

Mortgage-type repayments are calculated differently in different countries.  I think what you want is the US formula; see

http://www.mathsisfun.com/money/compoun … iodic.html

Bob

You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei

## #4 2013-06-03 22:11:44

SteveB
Power Member

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### Re: Struggling with calc of interest compounding monthly

I have just read the original post again, and I can see a bit which I did not read the first time:

This makes things a lot easier, and is not like a mortgage repayment because that is based upon the assumption
that repayments will be made each month which are taken off the loan (well it is in the case I was thinking of).

If I am understanding things correctly you are supposed to be doing something like this:

Let A = 200000  (The amount of the original loan.)
Let i = 14/(12 * 100)
So i = 0.01166666667 (to the accuracy of a calculator)
The extra division by 100 is to convert a percentage to a decimal.
The division by 12 is to convert into an amount per month.
(Strictly speaking the 12th power root should be taken, but appearently in USA conventions this is not
how it is done. Instead it is divided by 12 for simplicity and they do not worry about the fact that this
raised to the power of 12 is not the same when added to 1 and then 1 is subtracted at the end if you
see what I mean. Compare 1.01166666667^12 to 1.14 they are not the same.)
So if I add 1 to the value of i to represent adding 100%
F = i + 1
F = 1.01166666667

My variable of F is supposed to be the factor of increase in the amount owed per month of compounding.

Using my interpretation, and this is the bit that I do not know whether it is correct, we should do this:

Where n is the number of months in which interest is accumulated assuming no money is paid back.

I am getting: 430032.30

This assumes that there are n=66 months of accumulation. (Not sure whether this is correct.)

Last edited by SteveB (2013-06-03 22:16:04)

## #5 2013-06-04 17:56:21

mezzlepop
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### Re: Struggling with calc of interest compounding monthly

Thank you Bob Moderator for referral to the appropriate pages on your site.

And thank you Steve B for not only giving me the answer, but showing and explaining the method.  You rock !!!
That's exactly what I needed to know.

In the meantime I came across a "calculator site" which gave me exactly the same answer, so you calculation was perfect.
The difference is though, that because you showed your method, now I know how to do it myself in the future.

Thanks again.  Soooo much appreciated.

Mezzlepop

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