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# Yield Booster

One of the main incentives for staking $CRUIZE for$esCRUIZE is the ability to boost your rewards on the provided liquidity. $esCRUIZE tokens allow you to earn a boost of up to 25x on the yield generated on your provided liquidity. A total of 10,000,000$CRUIZE tokens will be reserved each year for these boosted rewards. The protocol will group users into 4 tiers depending on the below ratio,
$r=\frac{esCRUIZE\_held}{liquidity\_provided}$
where the multiplier associated with each tier is as follows:
• $r$
< 5% will receive a 1x multiplier
• 5% <
$r$
< 15% will receive a 4x multiplier
• 15% <
$r$
< 25% will receive 10x multiplier
• 25% <
$r$
In order to avoid exceeding the 10,000,000 yearly rewards limit, the following constrain must be achieved:
$\begin{gather*} ( users\_tier\_1*1*x)\\ +\ ( users\_tier\_2*4*x)\\ \ \ +\ ( users\_tier\_3*10*x)\\ +\ ( users\_tier\_4*25*x)\\ \ =\ 10,000,000 \end{gather*}$
where
$x$
constitutes the base reward rate. Therefore, the amount of returns to be augmented by each tier’s multiplier has to be:
$x=\frac{10,000,000}{\sum_{i=1}^4 (\text{\\users\_tier\_i * multiplier\_i})}$
for
$multiplier\_i$
= 1, 4, 10, 25 for
$i$
= 1, 2, 3, 4 respectively.

### Example

Let’s see this with an example. Let’s suppose the protocol configuration is as follows,
• $TVL$
= $10,000,000 • $APY$ = 10% • $APY\_after\_protocol\_fees$ =$830,000
• $CRUIZE\_price$
= \$0.3
Let's suppose that we have 4 users with the following percentages of LP provision and staked assets
• user 1: 10%
$liquidity\_provided$
; 1%
$esCRUIZE\_held$
$r$
= 0.1 ⇒ tier 2
• user 2: 10%
$liquidity\_provided$
; 1%
$esCRUIZE\_held$
$r$
= 0.1 ⇒ tier 2
• user 3: 10%
$liquidity\_provided$
; 1%
$esCRUIZE\_held$
$r$
= 0.1 ⇒ tier 2
• user 4: 70%
$liquidity\_provided$
; 97%
$esCRUIZE\_held$
$r$
= 1.38 ⇒ tier 4
Then the base APY generated on the total value staked by all users is 8.30% and the base reward rate of the APY is given by
$\begin{gather*} x\ =\ \frac{10,000,000}{( 3*4) \ +\ ( 1*25)} \ =\ 270,270\\ \end{gather*}$
which gives a final total APY of
• user 1: 8.30% +
$\frac{4*x}{10\% * 10,000,000}$
= 44.3%
• user 2: 8.30% +
$\frac{4*x}{10\% * 10,000,000}$
= 44.3%
• user 3: 8.30% +
$\frac{4*x}{10\% * 10,000,000}$
= 44.3%
• user 4: 8.30% +
$\frac{25*x}{70\% * 10,000,000}$
= 104.83%