APR rate

scmp.com... 1 Feb 2009

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Right now, if you were to purchase a 12-month US Treasury bond, the yield, or return, would be about 45 basis points. I will let you speculate why Hong Kong banks pay so much less interest than the yield on a US Treasury bond. I will offer one suggestion: it is because they can.

But what if the bank is lending you money? How much interest would you have to pay if you took out a personal loan? If you ask for a loan, the bank will quote you two interest rates: the monthly flat rate and the annualised percentage rate, or APR.

For example, if you want to borrow HK$100,000 for 12 months, the monthly flat rate will be about 0.5 per cent, while the APR will be about 11.5 per cent.

What will be immediately obvious is that the APR is not the monthly rate multiplied by 12. It is nowhere near that simple. In fact, I challenge any reader to ask a bank loan officer how the APR is calculated and see if you can understand the answer.

The APR is not the interest that the borrower will pay over a year, and it is not the average interest that the borrower pays each month. At the risk of lapsing into financial jargon, the APR is the discount rate applied to loan repayments so the net present value of those payments equals the original loan amount.

"Net present value", "discount rates" and the "time value of money" are subjects for college courses, so let us not go there.

The Hong Kong Association of Banks' code of banking practice mandates that banks quote the APR for loans. But the formula used to calculate it, in addition to being difficult to understand, is not particularly easy to find, either. And although this approach is theoretically correct, how a discount rate calculation is useful to anyone who does not have an MBA is difficult to understand.

And what about the monthly flat rate of 0.5 per cent? Does this number mean the borrower is paying 0.5 per cent interest per month? Well, kind of. The trick here is the "flat" part. Ordinarily you would assume that you pay interest to the bank on the outstanding loan balance, so that as the loan gets repaid, the interest payments drop. With a "flat" rate, borrowers pay the same amount of interest no matter how much of the principal they have repaid.

On our imaginary loan, the monthly payments would be about HK$8,800 per month. In the first month that would be about HK$8,300 of capital and HK$500 of interest, and the interest would be the stated flat rate of 0.5 per cent on the outstanding HK$100,000.

Each month the principal is reduced so that, in the sixth month, the borrower will only owe the bank HK$58,000, but will still make the same monthly payment of HK$8,300 of capital and HK$500 of interest. So this month the interest rate will be more like 0.85 per cent instead of 0.5 per cent. In the final month, when the outstanding principal is only about HK$8,300, the interest, still at HK$500, is 6 per cent per month. This way, the average effective monthly interest rate over the life of the loan ends up being three times as much as the flat rate.

So that is what flat means. The bank calculates the interest payable on the total loan and this amount stays flat every month, even though the loan decreases. To clarify this for the borrower, the bank gives you the APR - the net present value calculation - which of course does not clarify a great deal for most of us.

So how much interest does the borrower actually pay on our imaginary loan? After 12 months of HK$500 per month, you have paid HK$6,000. That would equate to 6 per cent if you never paid any of the capital back, but because the balance of the loan is not the same at the end as it was at the beginning, 6 per cent is less than what the borrower actually pays.

Based on the interest paid on the outstanding balance of the loan each month, the average interest per month that the borrower actually pays is 1.55 per cent, or 18.6 per cent a year. Unsurprisingly, this is a lot more than the flat rate and also a fair bit more than the APR.

And although I left it out of the calculation to keep it simple, there is also going to be an "administration" or "handling" fee of about 1 per cent.

Now the fact that the bank lends money at a higher rate than it borrows should not surprise anyone - that is the banking business. That the average interest rate is a bit higher than the advertised rate, well, that is probably not surprising either. But what is surprising is that even when the odds seem to be stacked firmly in the banks' favour, they somehow manage to lose so much money.