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

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%

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.
:-)

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

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.

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.

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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