$($Future value of an annuity$)$ Imagine that Homer Simpson actually invested the $$180,000$ he earne providing Mr$.$ Burns entertainment $9$ years ago at $9$ percent annual interest and that he starts investing an additional $$1,600$ a year today and at the beginning of each year for $15$ years at the same $9$ percent annual rate. How much money will Homer have $15$ years from today?

$($Annuity payments$)$ Calvin Johnson has a $$6,000$ debt balance on his Visa card that charges $13\mathrm{.}7$ percent APR compounded monthly. In $2009,$ Calvin's minimum monthly payment is $2$ percent of his debt balance, which is $$120.$ How many months $($round up$)$ will it take Calvin Johnson to pay off his credit card if he pays the current minimum payment of $$120$ at the end of each month? In $2010,$ as the result of a federal mandate, the minimum monthly payment on credit cards rose to $3$ percent. If Calvin made monthly payments of $180$ at the end of each month, how long would it take to pay off his credit card?

$($Present value of a perpetuity$)$ What is the present value of a $$1,000$ perpetuity discounted back to the present at $13$ percent?