You are given the following information: A deposit of $$100$ at time $0$ accumulates to $$114\mathrm{.}23$ in $3$ years The $6-$month spot rate $=4\mathrm{.}30\%($nominal annual rate compounded continuously$)$ f$(0\mathrm{.}50,1\mathrm{.}50)=5\mathrm{.}24\%($nominal annual rate compounded continuously$)$Compute the $1\mathrm{.}5-$year forward rate in $1\mathrm{.}5$ years $($f$(1\mathrm{.}50,3\mathrm{.}00))$ compounded continuously.HINT: the math is easier if you compute the interest rate earned over the $3-$year period as a nominal annual rate on a compounded continuous basis and use this rate to compute f$(2\mathrm{.}50,3\mathrm{.}00).$

Complete the problem and give me all the process with the numbers. Thank you!