$1.$ If you want to have $$500,000$ when you retire and you put $$85,000$ in your retirement account right now, and you can get an interest rate of $5\mathrm{.}2\%$ a year, how many years will it take you to achieve your goal?

$2.$ Sammy decides to set up a retirement fund. He deposits $$7,000$ a year. He earns an annual interest rate of $4\mathrm{.}5.$ How much will Sammy have in his retirement fund in $25$ years?

$3.$ Sammy wants to see what his retirement fund would be if he made $$7,000$ deposits at the first of every year instead of at the end. How much will Sammy have im his retirement fund in $25$ years at the rate of $4\mathrm{.}5\%$ if the deposits are made at the beginning of the year?

$4.$ Sammy wants to help a fellow small business owner. The other owner, Mr$.$ Noles offers to pay Sammy $$4,250$ a year for $8$ years in exchange for a loan of $$28,000.$ If the interest rate is $4\mathrm{.}2\%,$ is this a good investment for Sammy? What is the present value of this annuity?