Luke Smith wants to retire in 20 years. He expects to live for another 15 years after retirement. During retirement he wants to withdraw $12,000 at the start of each year from a savings account.

1) How much will he have to deposit in this savings account at the end of each year for the next 20 years, if the interest rate is 10%, compounded annually?

2) How would the deposits be changed if Mr. Smith expects his wife to live for another five years after his death, and he wants her to withdraw $6000 at the start of each year after his
death?