A worker aged $35$ wishes to accumulate a fund for retirement by depositing $$4,500$

at the beginning of each year for $30$ years. Starting at age $65$ the worker plans

to make $15$ annual withdrawals at the beginning of each year. Assuming that all

payments are certain to be made, find the amount of each withdrawal starting at

age $65,$ if the effective rate of interest is $9\%$ during the first $30$ years but only $7\mathrm{.}5\%$

thereafter.