A colleague and I have been discussing a way to find out the monthly interest rate charged by a credit card company against a given balance. Here's what we came up with...
Now we have worked out that £27.43 (the interest charged this month) is 1/12th of 15.9% of the balance which seems like a fair way to process the interest given that the balance changes from month to month.
However, if we compound the given value as a percentage it comes out not to 15.% apr but over 30% £27.43 is 1.329% of the balance. Compound this over 12 months and you get and APR of 30.359%
If the APR is stated as 15.9% we worked out (very roughly by a process of elimination) that the monthly interest should only be 1.2595% (which compounded to 15.93%). 1.2595% of the balance is only £25.99(545) which rounds to £26.00.
It seems the banks are doing us a favour by giving us an APR, but doing themselves a HUGE favour by dividing the APR by 12.
Now, I'm not out to discredit banks or credit card companies, but would like to understand how they do it so I can sleep at night! :)
You must have copied it down wrong and meant 1.2395% instead of 1.2595%. Try 1.237238% :-) You may well find that the contract rate is 1.2375% per month or 14.85% per year -- they don't work out what the monthly rate is by reference to the APR, they have a contract rate and compute the typical APR from that.
That's not what they're doing, it's coincidence. Anyway, it's more linke 15.948%.
Unless the balance of £2063.95 has been constant for a whole month since the last payment was made, and there have been no purchases since then, it doesn't make sense to work out what percentage of the balance is represented by £27.43. Bear in mind also that some purchases in the previous statement period may have been potentially interest free, but if not settled last month, then interest on them will run from the transaction date, and so the interest-generating period on part of the balance will be longer than a month.
They won't do it that way, they'll work it out on the balance on a daily basis, rather than just using the statement date balance. Also they'll take into account any interest free period (usually between purchase date and statement date).
No you don't. 1.329% monthly compounded over 12 months is 17.17%
1.01329^12 -1
I suspect the average balance during the month was higher than the statement date balance, explaining why the above is still higher than the quoted APR.
Ronald & Andy are both right and have pointed out your error.
The general rule for an APR is that it is that rate of discount which, when applied to a cash flow consisting of all the payments made under the credit agreement, results in an NPV equal to the amount borrowed.
The OFT provide some methods of calculations to make it simpler.
For Credit cards (being a form of running credit) the current rules are here :
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from which it shows that the APR for Credit Cards must assume a scenario which may be different from the actual use of the card and that the APR actually paid may be different from that quoted.
In particular " 1. In the case of an advertisement relating to running-account credit, the following assumptions shall have effect for the purpose of calculating the total charge for credit and any APR, notwithstanding the terms of the transaction advertised and in place of any assumptions in Part 4 of the Total Charge for Credit Regulations that might otherwise apply -
(a) the amount of the credit to be provided shall be taken to be £1,500, or, in a case where credit is to be provided subject to a credit limit of less than £1,500, an amount equal to that limit;
(b) it shall be assumed that the credit is provided for a period of one year beginning with the relevant date;
(c) it shall be assumed that the credit is provided in full on the relevant date;
(d) where the rate of interest will change at a time provided in the transaction within a period of three years beginning with the relevant date, the rate shall be taken to be the highest rate at any time obtaining under the transaction in that period;
(e) where the agreement provides credit to finance the purchase of goods, services, land or other things and also provides one or more of -
(i) cash loans
(ii) credit to refinance existing indebtedness of the debtor's, whether to the creditor or another person; and
(iii) credit for any other purpose,
and either or both different rates of interest and different charges are payable in relation to the credit provided for all or some of these purposes, it shall be assumed that the rate of interest and charges payable in relation to the whole of the credit are those applicable to the provision of credit for the purchase of goods, services land or other things;
(f) it shall be assumed that the credit is repaid -
(i) in twelve equal instalments, and
(ii) at monthly intervals, beginning one month after the relevant date"
How did you perform the calculation on the monthly rate to get the APR? is there a way of reversing this calculation to get the monthly rate from the APR?
As per John's post the APR is more complicated than the simply compounding the monthly rate. But this gives a good approximation. In any case the quoted APR will assume a particular cashflow pattern which may not match your use of the card.
Anyway compound interest is fairly simple... you first need to work out the interest factor, ie the rate at which the debt is growing, which is simply 1 + the rate, eg with a rate of 1.329% it's 1.01329.
This is how fast the debt is growing, so to work out compound interest over a year simply raise this factor to the power of 12. That's the annual factor, then take off
And to answer the other part of the question, i.e. "is there a way of reversing this calculation", yes, there is, and what you do is raise the annual factor to the power (1/12) to get the monthly factor (this is also known as taking the twelfth root).
Most "scientific" pocket calculators have a button marked either "X to the power -1" or "1/X" to achieve this. So if the annual compound rate is 17.167%, what you need to do is:
1.17167 (X to the power Y) 12 (1/X) (equals) and you get 1.01329 which means 1.329%.
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