# Formula for calculating APR from Monthly interest

I'm looking for a formula for calculating the APR of a loan from the monthly interest rate. Does anyone have the formula that should be used?
I've looked at a few websites but none seem to have this specific
feature available being mainly designed for mortgage calculations where the APR is already known.
Axel
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snipped-for-privacy@white-eagle.invalid.uk wrote:

(1+monthly_rate)^12-1
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Funny... a monthly interest rate of 1.19% yields an APR of approximately 12,170% according to your formula!
Axel
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snipped-for-privacy@white-eagle.invalid.uk wrote:

I make it about 15.25%
1.0119^12 = 1.15252711306
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In an earlier contribution to this discussion,

But you have to realise that "monthly rate" (and the resulting APR) are in the form of a *fraction* - not a percentage. 1.19% as a fraction is 0.0119
So 1.0119 ^ 12 = 1.1525
The APR as a fraction is thus 0.1525 - or 15.25%
--
Cheers,
Roger
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Roger Mills wrote:

correct

incorrect
Actually a percentage *is* a fraction, and therefore if a context requires a fraction, it can't reject a percentage.
In its simplest form, "%" is just shorthand for "/100", and so "1.19%" *is* "1.19/100" *is* "0.0119".
In a less simple context, such as where a percentage is added to something which isn't a percentage, then "+X%" is shorthand for "*(1+X/100)".
That's why "(1+monthly_rate)" is "1+1.19%" is "1*(1+0.0119)" is "1.0119".

That's misleading. Although 1.19% is indeed 0.0119, 1.19% expressed as a fraction can be not only 0.0119 but also 1.19%, because "1.19%", being a percentage, is *already* a fraction.

See? You got it right this time: either of 0.1525 or 15.25% qualifies as a fraction.
:-)
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Thanks guys.
It rather looks as if American Express is charging me more than their advertised rate (12,9%) for the Blue Credit Card.
Axel
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snipped-for-privacy@white-eagle.invalid.uk wrote:

That APR probably includes the effect of an interest free period for balance transfers if you take out the card.
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Ah. Explains much, especially as I did not have any balance transfers.
Just trying to compare it to my US AmEx card... 0% for six months and then 9.99% (excluding cash advances).
Axel
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In an earlier contribution to this discussion,

No, I got it *all* right! I was simply pointing out that you can't just take the *numeric* percentage value and plug it into the formula - otherwise you get (1 + 1.19) ^ 12 = 12,170 - which is clearly nonsense. But when you adjust the decimal point to account for the fact that % means "divided by 100", it all comes out right.
Expressed another way, all elements of the formula have to use the same *units* for it to work - and not mix 2 sets of units which are two orders of magnitude apart.
--
Cheers,
Roger
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"Roger Mills" wrote

No, you didn't. RR was correct when he pointed out that you saying "not a percentage" was actually *incorrect*.
"Roger Mills" wrote

Wrong again! There are *no* "units" in that formula! They are all just simple numbers...
The *units* will measure the currency - eg Pounds or Dollars etc.
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In an earlier contribution to this discussion,

I think we're arguing about semantics!
When the monthly rate is 1.19%, the value of (1 + monthly rate) to be used in the formula is 1.0119 *not* 2.19 - as used by one particular respondant.

Semantics again. What I was saying was that as soon as you put a % sign after a number, the 'units' in which that number is measured immediately become 1/100 of what they would be without the % sign. This may not be a conventional use of the word 'units' - but the effect is the same.
--
Cheers,
Roger
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Roger Mills wrote:

Since semantics means meaning, it's rather an important issue to be arguing about, wouldn't you say? In this case, unless one is clear about what "percentage" actually means, one is bound to get into difficulties.

Of course, but that's only because that particular respondent wasn't as au fait with fractions, rates, and percentages as the person who supplied the formula (reasonably) expected him to have been.

So what? Semantics are supremely important.

That's a bogus argument. Tim's right, there are no units in an interest rate, it is a dimensionless fraction. Percentages are just a special representation of fractions, in which their value is inflated by a factor of 100.
As soon as you try to do any arithmetic with fractions, then if the formula calls for a fraction to be plugged into it in a particular place, and if the fractions you wish to use happen to be represented as percentages, then clearly they must first be deflated before they can be plugged in, if you want correct results.
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In an earlier contribution to this discussion,

That's precisely what I was saying - in slightly different words - so what are we arguing about?
--
Cheers,
Roger
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Roger Mills wrote:

That your "slightly" different words were different enough to be wrong. :-)
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APR = 1+(monthly rate/12)^12-1
Marcus
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On Fri, 18 Aug 2006 03:37:29 GMT, "Marcus Fox"

Why do you divide the monthly rate by 12?
--
Peter Saxton from London
snipped-for-privacy@petersaxton.co.uk
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"Peter Saxton" wrote

Also - why does he both add one to, and subtract one from, "(monthly rate/12)^12"?! [Brackets in wrong place...]
Methinks he meant either:
APR = (1+monthly rate)^12-1
or:
APR = (1+yearly rate/12)^12-1
[Not that these would necessarily give the APR anyway!]
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