$1.)$ Shaun has been looking at houses. He has $$10000$ that he wants to invest, hoping that he can end up with $$15000$ to make a down payment on a house. He has an opportunity to invest at $6\mathrm{.}5\%$ simple interest, paid annually. How long will it take before Shaun can make a down payment of $$15000?$

$2.)$ A bank is offering a simple interest rate of $3\mathrm{.}2\%$ for a guaranteed investment certificate with a $5-$year term.

a$)$ What principal would you need to invest if you wanted to have $$20000$ at the end of the term?

b$)$ How long would it take for the value of the GIC to be $$25000?$