$4-87$ A $25-$year$-$old engineer is opening an individual

retirement account $($IRA$)$ at a bank. Her goal is to

accumulate $$1$ million in the account by the time she

retires from work in $40$ years. The bank manager

estimates she may expect to receive $6\%$ nominal

annual interest, compounded quarterly, throughout

the $40$ years. The engineer believes her income will

increase at a $5\%$ annual rate during her career. She

wishes to start her IRA with as low a deposit as pos$-$

sible and increase it at a $5\%$ rate each year. Assuming

end$-$of$-$year deposits, how much should she deposit

the first year?