Untold numbers of Citibank (NYSE: C) credit card users recently received a letter in the mail telling them that their interest rates will be increased, but part of their interest will be refunded if they pay their credit card bills each month.

Here’s what Citibank said in the letter to customers

Earn Interest Back Every Month.

Here’s how — make your payment on time every month. Each month you do, you will receive a credit on your billing statement equal to 10% of your total interest charge on purchase balances. This can help offset the increase in your purchase APR. Start earning interest back in December and January, and you will see the full credit on your statement no later than February 2010 and monthly after that.

If in any month you do not pay on time, you may not be eligible to continue to participate in this program.

Many Citibank customers that are in good-status and have paid their credit cards on time are having their interest rates raised on November 30th. Citibank is also rolling out a “rolling rebate” program which will give consumers a rebate on the last 10% of the interest they paid 90 days after the end of the month if the consumer continues to pay on time.

In essence, consumers that are given a new 29.99% rate will have a 26.99% interest rate with a 90day perpetual delay.

Citibank’s “rolling rebate” program is a new strategy in the credit card industry. The bank is hoping to encourage consumers to make their monthly payments on-time by offering the interest rate rebates, but consumers will actually paying more money at the end of the day because Citibank is simultaneously raising interest rates on their credit cards.

Customers that received these letters have had largely negative thoughts about the new rebate program. One reader of the Consumerist stated, “This seems very convoluted and is definitely annoying…This is too stupid to deal with.”