Credit card companies use several methods to calculate interest. There can be one or two billing cycles per month. Interest can be charged on the daily balance, new purchases, etc. You should refer to the "How finance charges are calculated" section of you billing statement.
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The formula for the daily compound interest is B=p(1+r over n)NT as an exponent for the nt B= ending balance P= principal amound r= interest rate n= number of compounds per year t= time( in years)
There is no carrot in the compound interest formula!
Formula to calculate the ratio
It depends on which compound interest formula you mean. Refer to the Wikipedia Article on "Compound Interest" for the correct terminology.
To calculate the interest gained on something, a simple formula is used. Initial value x (percentage increase as a decimal)^years So: 10000 x 1.05^15 = 20789.28 (2d.p).