$5.$A man is planning to retire in $37$ years. Money can be deposited in a retirement fund at $12\%$ interest compounded weekly and it is estimated that the future general inflation rate will be $3\%$ per year. He wants to make annual withdrawals of $100,000$ in terms of today's dollars over $30$ years of retirement. Assuming the first withdrawal occurs at the end of the first year of retirement.

How much money in terms of today's dollars should he have in this fund at the time of retirement?

What is the amount of the first retirement withdrawal in terms of today's dollars?

How much money in terms of actual dollars should he have at retirement?

How much is each quarterly deposit until retirement?