信用卡的「實際年利率」的計算公式為何?

是用Net Present Value方法及一些金管局定下的假設來計算。詳細資料及例子,可以到以下金管局2000年發出的文件找到：

http://www.info.gov.hk/hkma/eng/press/2000/attach/20001004e3a2.doc


圖片參考：http://upload.wikimedia.org/math/e/f/7/ef71162adba34ae9230be72bb5f6f705.png

NPV = original loan amount
n = number of instalments
Ct = monthly instalment amount
t = time interval, expressed in years, between the relevant date and the date of the kth instalment
r = unknown APR


The assumptions

10. Since the APRs calculated would depend on the behaviour of the cardholders (e.g. the repayment patterns), a set of assumptions must be made so as to provide a consistent basis for calculation. The guideline, “Credit Charges and APR”, issued by the Office of Fair Trading in the UK further sets out the assumptions which should be made and the types of fees and charges which should be included for calculating APRs. For credit card products, the following assumptions are relevant:

(i) A single amount of credit equal to the credit limit provided is withdrawn at the earliest time possible;
(ii) The amount of instalments is the smallest required under the agreement (i.e. 5% minimum repayments);
(iii) The borrower continues to make the minimum payments until the balance on the account falls to zero;
(iv) If the transaction requires a repayment to be made no later than a specified date, that date should be used as the time of repayment; and
(v) If there are repayments of credit or payments of charges which are to be paid before the relevant date (i.e. the end of the relevant period), it must be assumed that they are paid on the relevant date.
11. It is proposed that the assumptions provided for in the UK guideline should be followed as far as possible. However, certain adaptations are necessary to cater for the local practices. The following assumptions are recommended:

(i) The retail purchase is made or the cash advance is withdrawn at the earliest time possible (consistent with the UK guideline);
(ii) The amount of credit used is HK$50,000;
(This assumption is necessary because most card issuers levy fixed charges. If the amount of credit used is not specified, these fixed charges can translate into different APRs. Industry representatives in the Informal Working Group on Review of Code of Banking Practice (IWG) consider that a limit of HK$50,000 is reasonable in the context of Hong Kong’s credit card market.)
(iii) All fees and charges, with the exception of annual card fees, should be taken into account;
(This assumption is slightly different from that adopted in the UK where all fees and charges are included. Annual card fees are suggested to be excluded because they may often be waived in Hong Kong. It can also be argued that annual card fees do not form part of the cost of credit since a cardholder will need to pay the annual card fee regardless of he makes use of the credit facility or not. This is in line with the existing industry guideline on APR mentioned in paragraph 4 above.)
(iv) Bonus schemes and cash rebates are ignored since it is too difficult to translate such benefits into pecuniary terms (consistent with the UK guideline);
(v) All repayments of credit or payments of fees and charges are made at the end of each relevant period (consistent with the UK guideline); and
Cardholders make minimum payments until the outstanding balance falls to zero (consistent with the UK guideline)

Sample 1, If
P=Principle(10,000)
Interest Rate=2% per month
F=Finance Change(3%)

then,
F=Finance Change(3%)
10,000 x 3% = 10,300

first month:
10,300 + (10,300 x 2%) = 206

Second month
10,506 + (10,506 x 2%) = 10,716.12

similar, annual interest rate will be 27.6%


Example 2:
If
P=Principle(10,000)
Interest Rate=2% per month
F=Finance Change(Free)
then,
first month:
10,000 + (10,000 x 2%) = 200

Second month
10,200 + (10,200 x 2%) = 10,404.00

similar, annual interest rate will be 25.4%