$7.$On her $25$ th birthday, a young woman engineer decides to start saving toward building up a retirement fund that pays $6\%$ interest compounded monthly $($the market interest rate$).$ She feels that $$1,000,000$ worth of purchasing power in today's dollars will be adequate to see her through her sunset years after her $66$ th birthday. Assume a general inflation rate of $3\%$ per year.

Find the monthly deposit amount:

Living expenses raise by $4\%$ each year, find A$1$ for $22$ years after retirement:

Living expenses raise by $$8000$ each year, find $A1$ for $22$ years after retirement: