$1.$ What is the Future Value of $$13,000$ placed in a savings account for eight years given quarterly compounding with a nominal rate of $5\%?$

$2.$ You want to purchase a boat that costs $$30,500.$ You want to finance as much of the purchase as possible with a $6-$year bank loan with an APR of $8\mathrm{.}25\%.$ You can afford loan payments of $$425$ per month. How much will you need as a down payment to buy the boat? $($Round to the nearest dollar.$)$