The "divisible by nine" rule is a tradition that the People's Bank of China follows when it changes interest rates.
Readers may have been wondering why the People's Bank of China (PBoC) in April raised interest rates by 0.27%, rather than 0.25%, even though the macroeconomic effects of the two are essentially the same. A change of 27 basis points seems odd, particularly when there had been a long series of a quarter-of-a-per cent rises in the Fed funds target rate in the US.
The answer, interestingly, is tradition, which is reflected in the official guidelines for calculating interest rates on the Mainland. For instance, accounting standards issued jointly by the PBoC and the Ministry of Finance in 1993 and a notice on interest calculation issued by the PBoC to banks in 2005 specify how the annual, monthly, and daily rates should be derived from each other. These conversion rules were set based on the assumption that there were 360 days (rather than 365) and 12 months in a year, and always 30 days in a month. The daily rate is therefore the annual rate divided by 360 or the monthly rate divided by 30, and the monthly rate is the annual rate divided by 12. Traditionally, interest for loans and deposits with terms that do not fall neatly into whole years or months is calculated on a daily rate derived from the annual or monthly rate. The balance of the deposit or loan is then multiplied by the daily rate to give the interest. If the daily rate were to contain any recurring decimals, it would have to be rounded (up or down) to eliminate them, and any discrepancy due to the rounding would be carried over into the multiplication.
To avoid daily rates with recurring decimals, and the associated rounding complications in calculating the interest, annual interest rates (and any changes) have therefore to be divisible by 360. But since anything is divisible by 40 (provided you have enough decimal places for the exact answer), the annual interest rate, in practice, only needs to be divisible by nine. This, as far as I can ascertain, is the reason for the increase of 27 basis points (divisible by nine) in the benchmark lending rate by the PBoC on 27 April to 5.85% (also divisible by nine). Similarly, on 28 April, the five-year mortgage lending rate offered by the Housing Provident Fund was raised by 18 basis points to 4.14%.
Interestingly, some banks quote the annual interest rate in per cent (per hundred), the monthly interest rate in "per thousand" and the daily interest rate in "per ten thousand" to make the calculation of interest easier. One can simply multiply the number of years, months and days lapsed by the corresponding interest rates and the principal amount to get the interest amount.
As I understand it, the "divisible by nine" rule is a long-standing practice for setting interest rates in China. It is not difficult to see that this would make calculating interest more convenient if one was using an abacus instead of a calculator or computer. Perhaps this is why the tradition was established. Using an abacus to do division is a lot more difficult than to do multiplication, at least according to my own experience, particularly when one number is not divisible by the other. Although abacuses are not commonly used these days, the tradition lives on.
While the "divisible by nine" rule applies to renminbi deposits and loans, it does not affect how interest rates are determined for interbank borrowing and foreign currency deposits. But this minor inconsistency is definitely not a matter of earth-shaking importance that warrants eliminating the rule. It is a bit like using "wan", or "ten thousand", as a more convenient reference for an amount than "qian" or "thousand", in Chinese. As long as the method of calculation is clear, there should be no problem. Indeed, to change something for the sake of correcting a minor inconsistency can be problematic. So, the "divisible by 9" rule - now very much an interesting "trademark" of the PBoC since it applies the rule to other policy rates, including the central bank lending rate, the rediscount rate and the rates on required and excess reserves - continues to be a tradition of the financial system of the Mainland. It is also another small challenge for those wishing to understand finance in China.
Joseph Yam
29 June 2006
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