Understanding interest rates

lostcause82

I am a little confused about the interest rate on my mother in laws card. It says the monthly rate is 2.2071%. For the APR is it 12 times this?

grumbler

Approximately
The exact formula, that takes compounding into account, is (1+2.2071%)^12-1=29.95%

lostcause82

Thank you for working it out.

chattychappy

lostcause82 wrote: »

I am a little confused about the interest rate on my mother in laws card. It says the monthly rate is 2.2071%. For the APR is it 12 times this?

Very roughly, yes. 12 x 2.2071% = 26.5% (approx)

However this ignores compound interest. The correct calculation is:

Annual interest = ( (1 + monthly interest) ^ 12 ) - 1

So (expressing % as decimals):

Annual interest = ( (1 + 0.022071) ^12 ) - 1
Annual interest = 1.022071^12 - 1
Annual interest = 1.2995 - 1
Annual interest = 0.2995

So the correct APR is 29.95%

(If you are on Windows, you can use the built in calculator. Switch to "scientific mode". The "^" function is the button "xy".)

The error in using the 12x method increases with the interest rate. There are websites that do the calculation for you - but I think it's better to do the maths "for real" !