An investment of $1000 is to be used to make payments of $100 at the end of every year for as long as possible. If the fund earns an annual effective rate of interest of 5%, find how many regular payments can be made and find the amount of the smaller payment: (1) to be paid on the date of the last regular payment, (2) to be paid one year after the last regular payment, and (3) to be paid during the year following the last regular payment, as described in Section 3.6.