Lending Trade

Consider a Notional liquidity pool between DAI and 1-year DAI (fDAI maturing in one year), 6-month DAI (fDAI maturing in 0.5 years), 3-month DAI (fDAI maturing in 0.25 years):

Proportion (P) = fCash / (DAI + fCash) Exchange rate = ((1 / Scalar) * (ln(P / (1-P)))) + ((Anchor * time)+1) - (liquidityFee * time) Interest rate = (Exchange rate - 1) / Time Time = tenor span i.e. 1 = 1 year, 0.5 = 6 months and so on

Now let us assume you make a trade to buy 1000 fCash tokens

Proportion (P_n) = new fCash balance / (old DAI balance + old fCash balance) Exchange rate = ((1 / Scalar) * (ln(P_n / (1-P_n)))) + ((Anchor * time)+1) - (liquidityFee * time) DAI spent = fCash to be received / Exchnage rate = 1000 / Exchnage rate Interest rate = (Exchange rate - 1) / Time Time = tenor span i.e. 1 = 1 year, 0.5 = 6 months and so on

The pool and rates would look like this after the trade: