Formula for calculating APR from Monthly interest

(1+monthly_rate)^12-1

Funny... a monthly interest rate of 1.19% yields an APR of approximately 12,170% according to your formula!

Axel

APR = 1+(monthly rate/12)^12-1

Marcus

I make it about 15.25%

1.0119^12 = 1.15252711306

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%

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.

:-)

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

That APR probably includes the effect of an interest free period for balance transfers if you take out the card.

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.

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

Why do you divide the monthly rate by 12?

"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!]

"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.

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.

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.

That's precisely what I was saying - in slightly different words - so what are we arguing about?

That your "slightly" different words were different enough to be wrong. :-)