minor changes

Author: YaserJazouane

pages/home/oracle-integrity-staking/examples.mdx

@@ -16,14 +16,14 @@ $$
 {S^d_p} &= 0 \\
 {S^p} &= {S^p_p} + {S^d_p} = 100 + 0 = 100 \\
 {C}_p &= 500 \\
-\text{Total Amount eligible for Reward} \quad{E_p} &= min({S}_p, {C}_p) = min(500, 100) = 100 \\
-\text{Reward Rate (Yearly)} \quad{r} &= 10\% \\
-
-\text{Total Reward for one year} \quad{R_p} &= {r} \times {E_p} = 10\% \times 100 = 10 \\
-\text{Publisher Reward} \quad{R^p_p} &= {r} \times min({S^p_p}, {C}_p) = 10\% \times 100 = 10 \\
-\text{Delegator Reward} \quad{R^d_p} &= {R_p} - {R^p_p} = 10 - 10 = 0 \\
-\text{Effective Publisher Yield Rate} \quad{r^p_p} &= \frac{R^p_p}{S^p_p} = \frac{10}{100} = 10\% \\
-\text{Effective Delegator Yield Rate} \quad{r^d_p} &= \frac{R^d_p}{S^d_p} = \frac{0}{0} = 0\% \\
+\text{Total Amount eligible for Rewards} \quad{E_p} &= min({S}_p, {C}_p) = min(500, 100) = 100 \\
+\text{Annual Rate of Rewards} \quad{r} &= 10\% \\
+
+\text{Total Rewards for one year} \quad{R_p} &= {r} \times {E_p} = 10\% \times 100 = 10 \\
+\text{Publisher Rewards} \quad{R^p_p} &= {r} \times min({S^p_p}, {C}_p) = 10\% \times 100 = 10 \\
+\text{Delegator Rewards} \quad{R^d_p} &= {R_p} - {R^p_p} = 10 - 10 = 0 \\
+\text{Effective Publisher APY} \quad{r^p_p} &= \frac{R^p_p}{S^p_p} = \frac{10}{100} = 10\% \\
+\text{Effective Delegator APY} \quad{r^d_p} &= \frac{R^d_p}{S^d_p} = \frac{0}{0} = 0\% \\
 \end{aligned}
 $$
 
@@ -37,14 +37,14 @@ $$
 {S^d_p} &= 100 \\
 {S_p} &= {S^p_p} + {S^d_p} = 100 + 100 = 200 \\
 {C}_p &= 500 \\
-\text{Total Amount eligible for Reward} \quad{E_p} &= min({S}_p, {C}_p) = min(500, 200) = 200 \\
-\text{Reward Rate (Yearly)} \quad{r} &= 10\% \\
-
-\text{Total Reward for one year} \quad{R_p} &= {r} \times {E_p} = 10\% \times 200 = 20 \\
-\text{Publisher Reward} \quad{R^p_p} &= {r} \times min({S^p_p}, {C}_p) = 10\% \times 100 = 10 \\
-\text{Delegator Reward} \quad{R^d_p} &= {R_p} - {R^p_p} = 20 - 10 = 10 \\
-\text{Effective Publisher Yield Rate} \quad{r^p_p} &= \frac{R^p_p}{S^p_p} = \frac{10}{100} = 10\% \\
-\text{Effective Delegator Yield Rate} \quad{r^d_p} &= \frac{R^d_p}{S^d_p} = \frac{10}{100} = 10\% \\
+\text{Total Amount eligible for Rewards} \quad{E_p} &= min({S}_p, {C}_p) = min(500, 200) = 200 \\
+\text{Annual Rate of Rewards} \quad{r} &= 10\% \\
+
+\text{Total Rewards for one year} \quad{R_p} &= {r} \times {E_p} = 10\% \times 200 = 20 \\
+\text{Publisher Rewards} \quad{R^p_p} &= {r} \times min({S^p_p}, {C}_p) = 10\% \times 100 = 10 \\
+\text{Delegator Rewards} \quad{R^d_p} &= {R_p} - {R^p_p} = 20 - 10 = 10 \\
+\text{Effective Publisher APY} \quad{r^p_p} &= \frac{R^p_p}{S^p_p} = \frac{10}{100} = 10\% \\
+\text{Effective Delegator APY} \quad{r^d_p} &= \frac{R^d_p}{S^d_p} = \frac{10}{100} = 10\% \\
 \end{aligned}
 $$
 
@@ -58,14 +58,14 @@ $$
 {S^d_p} &= 300 \\
 {S_p} &= {S^p_p} + {S^d_p} = 300 + 300 = 600 \\
 {C}_p &= 500 \\
-\text{Total Amount eligible for Reward} \quad{E_p} &= min({S}_p, {C}_p) = min(500, 600) = 500 \\
-\text{Reward Rate (Yearly)} \quad{r} &= 10\% \\
-
-\text{Total Reward for one year} \quad{R_p} &= {r} \times {E_p} = 10\% \times 500 = 50 \\
-\text{Publisher Reward} \quad{R^p_p} &= {r} \times min({S^p_p}, {C}_p) = 10\% \times 300 = 30 \\
-\text{Delegator Reward} \quad{R^d_p} &= {R_p} - {R^p_p} = 50 - 30 = 20 \\
-\text{Effective Publisher Yield Rate} \quad{r^p_p} &= \frac{R^p_p}{S^p_p} = \frac{30}{300} = 10\% \\
-\text{Effective Delegator Yield Rate} \quad{r^d_p} &= \frac{R^d_p}{S^d_p} = \frac{20}{300} = 6.67\% \\
+\text{Total Amount eligible for Rewards} \quad{E_p} &= min({S}_p, {C}_p) = min(500, 600) = 500 \\
+\text{Annual Rate of Rewards} \quad{r} &= 10\% \\
+
+\text{Total Rewards for one year} \quad{R_p} &= {r} \times {E_p} = 10\% \times 500 = 50 \\
+\text{Publisher Rewards} \quad{R^p_p} &= {r} \times min({S^p_p}, {C}_p) = 10\% \times 300 = 30 \\
+\text{Delegator Rewards} \quad{R^d_p} &= {R_p} - {R^p_p} = 50 - 30 = 20 \\
+\text{Effective Publisher APY} \quad{r^p_p} &= \frac{R^p_p}{S^p_p} = \frac{30}{300} = 10\% \\
+\text{Effective Delegator APY} \quad{r^d_p} &= \frac{R^d_p}{S^d_p} = \frac{20}{300} = 6.67\% \\
 \end{aligned}
 $$
 
@@ -87,10 +87,10 @@ $$
 \quad{R^p_p} &= {r} \times min({S^p_p}, {C}_p) = 10\% \times 200 = 20 \\
 \quad{R^d_p} &= {R_p} - {R^p_p} = 50 - 20 = 30 \\
 \text{Fee paid by Delegator} \quad{F^d_p} &= {f} \times {R^d_p} = 2\% \times 30 = 0.6 \\
-\text{Final Delegator Reward} \quad{R^d_p} &= {R^d_p} - {F^d_p} = 30 - 0.6 = 29.4 \\
-\text{Total Publisher Reward} \quad{R^p_p} &= {R^p_p} + {F^d_p} = 20 + 0.6 = 20.6 \\
-\text{Effective Publisher Yield Rate} \quad{r^p_p} &= \frac{R^p_p}{S^p_p} = \frac{20.6}{200} = 10.3\% \\
-\text{Effective Delegator Yield Rate} \quad{r^d_p} &= \frac{R^d_p}{S^d_p} = \frac{29.4}{300} = 9.8\% \\
+\text{Final Delegator Rewards} \quad{R^d_p} &= {R^d_p} - {F^d_p} = 30 - 0.6 = 29.4 \\
+\text{Total Publisher Rewards} \quad{R^p_p} &= {R^p_p} + {F^d_p} = 20 + 0.6 = 20.6 \\
+\text{Effective Publisher APY} \quad{r^p_p} &= \frac{R^p_p}{S^p_p} = \frac{20.6}{200} = 10.3\% \\
+\text{Effective Delegator APY} \quad{r^d_p} &= \frac{R^d_p}{S^d_p} = \frac{29.4}{300} = 9.8\% \\
 \end{aligned}
 $$