A systems engineer named Allan is initiating a plan offering a $12\%$ interestrate compounded quarterly accumulates funds in an account over the next $35$ years to support a retirement plan that involves $30$ annual withdrawals commencing at end of $36$ th year. Initial withdrawal of $$200000$ with them increasing $8000$ annually. Anticipates a $3\%$ yearly increase in annual income. During working career begin with deposit. at end of first year and increase deposit by $3\%$ each year.

a$.$ How much money Alan must have in retirement account. $$ need initial deposit amount.

b$.$ amount of Allan's first deposit

c$.$ Determine future value of all Allan's withdrawals