Q$9.$ Save X dollar a month until retirement so that you can withdraw $$100,000$ lump sum when you retire $($i$.$e$.,$ stop working$)$ at the age of $80$ to travel around the world in $80$ days $($you are a fan of Jules Verne$)$ and also withdraw $$7,500\mathrm{.}00$ at the end of every month for $15$ years after you retire at $80.$ No money will be left in your saving account after you withdraw the last $$7,500$ at the end of $15$ years $($at $95$ years old$).$ You are $30$ years old now and you will retire at $80.$ Your saving account yields $18\mathrm{.}5\%$ per year compounded monthly. What is X $?$