(a) Assume that Luke Smith wants to retire in 20 years. He expects to live for another 15 years after his retirement, and during retirement he wants to draw $12,000 at the beginning of each year from his savings account. How much will he have to deposit in his account at the end of each year for the next 20 years, given that the interest rate is 10 percent compounded annually?

_______________________

(b) How would the amount computed under (a) be altered if Mr. Smith expects his wife to live for 5 years after his death and if, in addition to the amounts provided for under (a) he wants her to be able to draw $6,000 at the beginning of each year during this additional period?

Do not round any intermediate calculations. Final dollar answers may be rounded to two decimal places (e.g., $125.89). Other answers may be rounded to 8 decimal places (e.g., .12345678 or 12.345678%. if the problem does not specify an interest rate, assume the rate to be 12%.