(1) Stacey and her husband David have a joint savings account that earns 3.5% interest payable continuously and has a current balance of $58,458. Each year, David wishes to withdraw $4,000 payable continuously at a level rate. Stacey wishes to deposit X at the beginning of each year (for thirty years) so that the account will last for thirty years. What is the least X that will work?

(2) Bob deposits $1,500 at the beginning of each quarter for sixteen years in a fund earning a nominal rate of interest of 6% convertible monthly. The interest from this fund is paid out monthly and can only be reinvested at an effective annual rate of 5.2%. This is just as in Problem (4.5.5). Find Bobs yield rate for the twenty-year period.

(3) Payments of $5,000 are made into a fund at the beginning of each year for ten years. The fund is invested at an annual effective rate of i. The interest generated is reinvested at 10%. The total accumulated value at the end of the ten years is $100,000. Find i .