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Interest and economics

SWEEP is a dollar-denominated coin with a USD target price. Interest accrues from the change in the target price of SWEEP. Each week, the protocol sets a new and slightly higher target price for SWEEP that will take effect at the end of the week.
Borrowers pay this change in price. They borrow X SWEEP to make an investment. Then they buy back X SWEEP when they repay, often at a higher price.
For example, an interest rate of 4% leads to a weekly target price change of 1-1.04^(1/52), or 0.0755%
The interest rate can change each week. Sweep protocol moves the interest rate to balance demand for savings with demand for investment.

Mechanics

Borrowers have an incentive to supply SWEEP and invest the proceeds if they expect that their investment return will be greater than the SWEEP interest rate.
Over the medium and long term, the protocol needs to find a balance between the demand for savings, and the demand for investment. It does this by adjusting the target interest rate.

Short term dynamics

If savers are buying SWEEP, then the amount of SWEEP offered in the AMM (and weekly auction) will decline. The price will rise above target if <SWEEP amount>*<target price> < USDx amount.
In this case, borrowers will have an incentive to borrow and supply SWEEP, because they will experience a negative interest rate if the market price declines to the target price.
If savers are selling SWEEP, then the amount of SWEEP offered in the AMM (and weekly auction) will increase. The price will fall below target if <SWEEP amount>*<target price> > USDx amount.
In this case, borrowers will have an increased incentive to repay SWEEP, because they can buy it back for less than the expected price.
These incentives will work if Sweep protocol can credibly peg SWEEP to the target price.