monthly to annual interest rate conversion

ricklecoat

My maths stinks. Simple as that.
But I'm pretty sure that converting a monthly interest rate (as shown on my credit card statements) into an annual one for easier comparison (AER?) is not as simple as just multiplying it by 12 — compound interest being what it is, and all.

Does anyone have a formula to convert monthly rates to annual?
Cheers!

Joe_Bloggs

Compounding things is a problem as is putting interest rates into a calculator. 2.08% is really 2.08/100 or 0.0208. The '/' symbol standing for divide.
The interest for a month is the amount owed times the monthly interest rate. The total amount owed is the original amount plus the original amount times the interest rate.
Total owed = Original + Original x interest rate
We can factor out the original amount as it appears twice.
Total owed = Original (1 + interest rate)

Assume the multiply opertion if no operation is shown. Work out the contents of the brackets first.

For the next month the the same calculation takes place and we end up with
Total owed = Original (1+ interest rate)(1+ interest rate)
A pattern emerges of Original(1+ interest rate)^12 for 12 months. Where the ^ represents the to 'the power of key' . Eg 5^3 is just 5x5x5.This key is often labled x^y.
Going back to the original example of 2.08% per month over 12 months the amount would be (1 + 0.0208)^12 = 1.2802. Subtract 1 to represent the original amount and the 0.2802 left is the interest factor. Multiply by 100 to get 28.02% The original amount did not matter in the the end as we just wanted an annual interest rate from a monthly one.
J_B.

ricklecoat

J_B:

Thanks for that explanation, it makes perfect sense. I just used it to change all my credit card monthly interest rates into AER rates -- a frightening exercise in itself!

Certainly makes it obvious why they choose to put the monthly amount on the statements; people are used to seeing AERs quoted for loans, etc., in TV ads and so a monthly rate of 1.4566% feels, at first glance, quite low. Of course it translates into 18.95% AER which is rather less heart-warming.

Thanks again for your help; I'll make a note of the calculation formula for future reference.

Rick

Lexis200

very useful post Joe_Bloggs, thanks.

As a side note to anyone else who sees this post, an easy way to work the calculation out is to open google (https://www.google.co.uk) and copy/paste the formula into the search box ( (1 + 0.0208)^12 in Joe's example)... change the 208 to whatever your monthly interest rate is, and hit search.

Google has some powerful calculation features... in fact you can do it for all sorts of things, weights distances ("how many square inches in an acre"), see http://www.google.co.uk/intl/en/help/features.html#calculator for more details

HTH

CLAPTON

but rough and ready for mid range APRs multiplying by 13 give a pretty good approximation

e.g.

1% monthly is 12.68% but x13 is 13%
1.5% is 19.56 but x13 is 19.50%
2% is 26.82 but x13 is 26.00%
2.5% is 34.49 but x13 is 32.50%

not quite right but not too bad.

Fahim_2

Really useful post, joe, thanks.....

antuk

This maybe a stupid question but is there an easy way to do this in reverse, ie work out what the monthly rate of interest you will be charged is from the AER or APR

CLAPTON

not a syupid question

but dividing by 13 is a reasonable approximation

alternatively ...express the APR as a decimal i.e. if apr is 25.8% write this as 0.258 then add 1 (making 1.258) , take the 12th root (use calculator or excel or whatever) then substract 1.

but dividing by 13 is easier..and anyway why do you need it that accurate anyway.