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Calculating APR

Hello
I'm doing some work on calculating APR and i am reading this document


http://www.creditunion.ie/files/file_20050316024652OFT%20-%20Credit%20Charges%20and%20APR.pdf

Could i ask what this means on the bottom on page 45

"As this equation shows, at the correct annual rate, the present value of the
repayment is equal to the amount advanced. This is generally referred to as
the ‘present value rule’"

To me this is saying that PV = A at the 'correct annual rate'

What does it mean 'correct annual rate'?

To me PV = A when (1+i)^t is equal to 1

Is this what it is saying? I do not understand what it means by correct annual rate
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andieje
Asked:
andieje
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3 Solutions
 
Kevin CrossChief Technology OfficerCommented:
As you will note in your other question, some of the Experts showed you PHP implementations using IRR function.  The internal rate of return usually goes with NPV (net present value).

http://en.wikipedia.org/wiki/Net_present_value#Formula

Therefore, you are seeking the present value of the advance (A) here.  In other words, the present value of the advance equals the present value of the annuity payment at a specific rate of return.  If you do not use the correct interest rate, these values will not equal.
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andiejeAuthor Commented:
Hi,
I am going through the booklet in the other question as I don't understand the answers and that led to this question. I'm really sorry for being stupid but I don't really get it. I don't know anything about loans and finance so I don't even know the terminology. So to be honest, I'm just as confused by your answer  - if not more :(  sadly - as you have used slightly different terminology from the booklet. Perhaps I now need to open a different question to clarify the terminology but I know the quality of the forum is important and I dont want to create a jumbled heap of questions.

I've obviously misunderstood but i thought it meant PV was the value you borrowed and A is essentially the amount you are going to pay back in total, but the booklet then refers to PV as the 'present value of the repayment.' In your answer you also refer to 'present value of advance' which further confounds me as this isnt a term in the explanation of the previous pages either.

Thanks for answering
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Kevin CrossChief Technology OfficerCommented:
I understand the confusion as I myself had difficulty interpreting what the formula was after in your other question.  I explained PV and A in the way you understand it.  I was focusing on present and future values.  However, the booklet mentions you will get a list of payments and advances.  I caught this, but did not jump to annuity concept/formulas until I saw the code samples from the PHP Experts that both solved problem using an IRR function.  

I think their interpretation is a good path to explore.  In essence, it appears you have an annuity that you make payments to and receive advances for.  Maybe I am reading it wrong, but it would appear you need to find the interest rate (IRR) that makes the net present value (NPV) 0.

The link to the wiki page on NPV should help.
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andiejeAuthor Commented:
Hi Kevin
I've looked at their answers and it makes sense. The problem I am having is that I dont really understand this field and I really dont know how far i need to understand it either to just implement something. I get different answers on every online calculator/excel spreadsheet i try for even for simple loan repayment calcualtions (i've got another question on this) yet alone apr calculations. But then the loan repayment calculations feed into the apr calculation. Furthermore I get different answers depending on whether i use binary chop or newton rhapson for apr. It seems a minefield!
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Ray PaseurCommented:
When there are competing alternative investments, we need a way to standardize the values so that they can be compared on an "equal footing."  For example, when considering whether to buy a piece of real estate or invest in a savings bond, you would make some assumptions about the timing and amounts of the investments, when you would recover your cash, etc.  These assumptions can be put into calculations so that very different sets of cash flows can be compared.  One of the most common comparisons is the Internal Rate of Return.  The IRR concept assumes that you would prefer to have your money today, and that you would willingly delay that gratification if the future reward exceeded some threshold.

Understanding Net Present Value and Internal Rate of Return in various forms is basically the first year of business school.  It can be very simple, such as calculating the yield on a bond bought at discount and redeemable at par some years later.  Or it can be as complex and uncertain as buying a rental property, where there may be many cash flows, both in and out, representing the purchase price, taxes, rents and gross uncertainties (what if the tenants cause a fire?).  The Net Present Value is a measure of the magnitude of the investment.  The Internal Rate of Return is a measure of the yield, where higher numbers are better.

I haven't read all of it, but this article looks pretty accurate.
http://en.wikipedia.org/wiki/Internal_rate_of_return
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