with n = (i+1) > 0, n is the number of periods
rewards{0} = rsrRewards()
payout{i+1} = rewards{i} * payoutRatio
rewards{i+1} = rewards{i} - payout{i+1}
rewards{i+1} = rewards{i} * (1 - payoutRatio)
// Furnace.sol
// Paying out the ratio r, N times, equals paying out the ratio (1 - (1-r)^N) 1 time.
uint192 payoutRatio = FIX_ONE.minus(FIX_ONE.minus(ratio).powu(numPeriods));

uint256 amount = payoutRatio * lastPayoutBal / ratio;
// StRSR.sol
uint192 payoutRatio = FIX_ONE - FixLib.powu(FIX_ONE - rewardRatio, numPeriods);

// payout: {qRSR} = D18{1} * {qRSR} / r
uint256 payout = (payoutRatio * rsrRewardsAtLastPayout) / rewardRatio;
