Ferguson builds a binomial interest rate tree for a bond valuation. The one$-$year, two$-$year,$$and three$-$year par rates are $4\mathrm{.}00\%,5\mathrm{.}00\%,$ and $6\mathrm{.}00\%,$ respectively. Interest rate volatility$$is assumed to be $10\%.$ He follows the following steps: Step $1$: estimate the spot rates curve by bootstrapping. Step $2$: estimate $1-$year forward rate for each period by using no profitable arbitrage condition. Step $3$: build a binomial interest rate tree based on estimated forward rates under the$$assumption that interest change moves following log$-$normal distribution. Calibrate the binomial$$tree with$$the help of par rates. Fill in the blank $($#$1),($#$2),($#$3)$ and $($#$4).($Answer in percentage terms keeping four digits after the$$decimal without the $\%$ sign$)$ Answer: $($#$1)$:$$R$$ponse $1$ Question $1\%($Formulate the equation needed to solve for the $3-$year spot rate using the bootstrapping method and provide it in the answering box$)($#$2)$:$$R$$ponse $2$ Question $1\%($Formulate the equation needed to solve for this forward rate using the no$-$profitable$-$arbitrage condition and provide it in the answering box.$)($#$3)$:$$R$$ponse $3$ Question $1\%($Provide the formula in the answering box.$)($#$4)$:$$R$$ponse $4$ Question $1\%($Provide the Excel file demonstrating calibration using relevant par bond.$)$