1. (a) Suppose you start investing $0.25 per day from the day you are born. Assume that each year has 365 days and that you can invest at the rate of 11.83% (the average annual effective market return for US stocks from 19631993) without transaction costs. On your 65th birthday, how much money will you have (including the payment on that day)?

(b) Suppose each year on your birthday your daily investment amount increases by $0.25. What is the total value of your investment on your 65th birthday?

(c) On your 65th birthday you retire. You convert the sum in (b) into an annuity (assuming the same investment rate), with the first annual payment on your 66th birthday and the final payment on your 90th birthday. What is the amount of the annual payment?

Solve without excel. If using excel, provide formulas.