A card installment plan's APR runs higher than its flat monthly rate suggests

If a credit card installment plan charges interest each month as a fixed percentage of the original amount, you pay the same interest every month, even though the principal you owe the bank gets smaller with every payment. Announcement [2021] No. 3 of the People's Bank of China (PBOC) says an annualized rate must compare the total cost of a loan with the principal you actually have the use of, and for loans repaid in installments that means the principal left after each payment. Worked out this way, the annual rate comes out well above the per-installment rate × 12.

When you take out an installment plan, you don't have to guess this number. China's 2022 credit card rules require banks to show every interest and fee item, the annualized rate and the way interest and fees are calculated, prominently, on the first page of the installment contract and on the screen where you apply. The cost of borrowing has to be called interest, not a handling fee. When comparing plans, go by the figure marked as the annualized rate; if all you can see is a per-installment rate, put the payment amount into one Excel function and work the annual figure out yourself.

Multiplying the per-installment rate by 12 understates the cost

Take a hypothetical plan; the numbers don't reflect any bank's actual pricing. You put a 12,000-yuan purchase on a 12-month installment plan, each installment carries interest of 0.6% of the full amount, and the principal is split evenly across the 12 months.

The 7.2% figure assumes you hold the full 12,000 yuan for the whole year. In fact you only have all of it during the first month. After that, each payment cuts what you owe by 1,000 yuan, yet the interest is still 0.6% of 12,000:

The further into the plan you are, the less principal that same 72 yuan of interest is paying for, and the higher the true cost of the money. Capturing that is the whole point of an annualized rate.

To count the principal you actually hold in each period, the annex to the PBOC announcement uses the internal rate of return (IRR) method: find the monthly rate r at which the twelve payments of 1,072 yuan, discounted back to the day you borrowed, add up to exactly the 12,000 yuan you received.

12,000 = 1,072 ÷ (1 + r) + 1,072 ÷ (1 + r)² + … + 1,072 ÷ (1 + r)¹²

Solving gives r ≈ 1.086%, the monthly rate measured on the principal still owed. There are two ways to turn that into an annual rate:

• Compounded: (1 + 1.086%)¹² − 1 ≈ 13.84%, the IRR method used in the announcement's annex
• Simple: 1.086% × 12 ≈ 13.03%, which the announcement allows as long as it is labelled as simple interest

Both are far above 7.2%. The gap comes from the principal shrinking month after month while the interest stays put. The compounded figure is a little higher than the simple one because it rolls the monthly rate forward one month at a time across the year, picking up interest on interest along the way.

The PBOC rule for annualizing installment rates

The rule comes from PBOC Announcement [2021] No. 3, which requires every loan product to disclose an annualized rate, and applies to deposit-taking financial institutions, consumer finance companies and microlenders alike. The provision that matters for installments says that where principal is repaid in installments, the principal actually in use is the amount remaining after each payment.

The announcement breaks the annualized rate down into a few parts:

• Numerator: every loan cost charged to the borrower, covering interest and any fees directly related to the loan
• Denominator: the principal actually in use, with the amount stated in the loan contract or other debt instrument
• Method: compound or simple both qualify, compound meaning the IRR method; a simple-interest figure has to be identified as such
• Display: the annualized rate must be shown prominently in marketing and stated in the contract; daily or monthly rates can appear alongside it but should not be more prominent

The annex works through the IRR method with three examples. Its figures are reproduced as published:

In the third example the installment fee is charged every month as a fixed share of the original principal while the principal is repaid evenly, the same structure as the hypothetical plan in the previous section. 0.5% a month sounds low, yet the annex puts the all-in annual rate at about 12.80% simple or 13.58% IRR, and that includes the 1,000-yuan service fee paid up front. The mortgage example shows that the same loan produces a different annual figure depending on whether it is stated as simple interest or as IRR.

Working out your own plan's APR in Excel or WPS Spreadsheets

You need three numbers: the installment principal, the number of installments and the payment per installment. For the payment, use the total of principal plus interest; your statement lists it. Then type into any cell:

1. Monthly rate: =RATE(number of installments, -payment, principal). For the example, =RATE(12,-1072,12000), which gives about 1.086%.
2. Compounded annual rate: =(1+RATE(12,-1072,12000))^12-1, about 13.84%.
3. Simple annual rate: multiply the result of step 1 by 12, about 13.03%.

Don't drop the minus sign in front of the payment. If the principal and the payment carry the same sign, the function can't find an answer and returns an error.

Try another set at 0.75% per installment: interest is 12,000 × 0.75% = 90 yuan, each payment is 1,090 yuan, and multiplying by 12 gives 9%. Enter =(1+RATE(12,-1090,12000))^12-1 and you get about 17.48%.

Any fee you pay up front when the loan is drawn should come off the principal before you enter it, because you never really got that money. Try it on the annex's third example: =(1+RATE(12,-8833.3,100000-1000))^12-1 gives about 13.58%, matching the IRR in the annex.

If the payments aren't all the same, for instance the first one includes an extra charge, RATE won't work. List the cash flows in a column instead: the principal you received in the first cell (as a positive number), then each installment's payment in the cells below (as negative numbers). =IRR(that column) gives the monthly rate, which you annualize the same way as above.

Where does the APR appear on the contract and application screen?

In July 2022 the China Banking and Insurance Regulatory Commission and the PBOC issued the Notice on Further Promoting the Regulated and Healthy Development of Credit Card Business (CBIRC Rules [2022] No. 13), which has a section devoted to installments. The provisions that bear directly on interest are these:

• Each installment plan must be applied for and approved separately in advance and have its own contract, not mixed or bundled with contracts for other credit card services
• The first page of the contract and the application screen must prominently show every interest and fee item the plan may incur, the annualized rate and how interest and fees are calculated
• The cost of borrowing must be presented as interest, with clear rules on how it accrues, and not as a handling fee or similar, unless laws or regulations provide otherwise
• Banks may not offer only, or pre-select, an option that collects the full installment interest in one go

On the application screen, you can check these one at a time:

1. What the figure marked as the annualized rate is, and whether it says simple interest next to it;
2. Which fees are listed besides interest. Under the PBOC announcement, every fee directly related to the loan belongs in the numerator of the annualized rate;
3. Whether interest is charged with each installment or all at once. If it is all taken with the first installment, you pay earlier, and the same total interest works out to a higher annual rate. Under the rules this can't be the only option and can't be ticked by default, so look at which one is selected before you confirm;
4. Take the payment per installment shown on the screen, run it through the functions in the previous section, and compare your result with the annualized rate on the page.

If you can't spot the annualized rate on the application screen, turn to the first page of the installment contract; the rules require it in both places. If it's in neither, or it doesn't match the figure you worked out, call your card issuer's credit card customer service and ask what the annualized rate on this plan is, whether it is simple or compound, and how interest and fees are calculated. The same notice also requires banks to tell customers where to take enquiries and complaints, so that route is open if you still can't get a clear answer.

The wording on statements has changed too. Bank of China announced that from 4 December 2022 the installment fee on its credit cards would be called installment interest, and the installment fee rate would be called the installment interest rate. The change covered statement, purchase, cash and car installments among others, and the announcement stated that the annualized rate and the actual amount due each installment would stay the same. Only the name changed, not what you pay each month, so the annualized figure is still the one to compare.

Paying off early, minimum payments and overdraft interest

How is interest charged if I pay off an installment plan early?

Under China's 2022 credit card rules, if you settle an installment plan early, the bank should charge interest based on the amount of money you actually used and for how long; fees are charged according to laws, regulations and the contract. Before paying off early, look at what the installment contract says about early settlement and which fees it may charge besides interest.

Can I pay just the minimum on a credit card installment plan?

Under the 2022 rules, banks may not offer a minimum-payment option on installment plans, and may not put a balance that is already on an installment plan onto a new one, except under an individually agreed installment repayment arrangement. Each installment has to be paid in full as the contract sets out; if you're struggling, contact the issuing bank directly and explain your situation.

Does overdraft interest on a minimum payment also have to show an APR?

Overdraft rates also have to be shown as an annualized rate. Under the PBOC's Yinfa [2020] No. 327, from 1 January 2021 credit card overdraft rates are set by agreement between the issuer and the cardholder, which removed the old cap of 0.05% a day and the floor of 0.7 times that cap. When disclosing them, issuers must show the annualized rate prominently and may not show only a daily rate or a daily repayment amount.

Read more notes first

We are an independent third-party information site, not the official Binance website. The rules described here follow the original texts of PBOC Announcement [2021] No. 3 and the Notice on Further Promoting the Regulated and Healthy Development of Credit Card Business as published on the Chinese government's website, the PBOC's notice on market-based reform of credit card overdraft rates, and Bank of China's announcement renaming installment fees. The 12,000-yuan, 12-installment examples at 0.6% and 0.75% per installment are hypothetical and don't reflect any bank's actual rates. This article only explains how to work out what an installment plan costs; it is not lending or investment advice.