please work this out for me...?

Question

if interest on a credit card is 30.9% and costs £257.78 over 365days what is the credit limit?

Answer 1

You don't necessarily know what the credit limit is, but you can calculate the (average) balance over the course of the year from the annual rate and annual interest amount.

If you assume that the person has charged their credit card up to the credit limit, and that the balance didn't change during the year, then those two numbers are the same. Then the principal balance that you compute is the same as the credit limit. If you can't make that assumption, you can't compute the credit limit from the numbers given.

If you're doing simple annual interest, not compounded, it's:

interest = principal * rate
257.78 = p * 0.309
p = 357.78 / 0.309
p = 1,157.86

Otherwise, if you're doing monthly compounding, it would be something like:

prin + int = prin * (1 + rate-per-period)^periods
p + 257.78 = p * (1 + annual_rate/12)^12
p + 257.78 = p * (1.02575)^12
p + 257.78 = p * 1.3567
257.78 = 0.3567 * p
p = 722.59

Note how big a difference monthly compounding makes.