$1.$ Peter Chan has deposited $$20,000$ in a guaranteed investment account with a promised rate of $5\%$ compounded annually. He plans to leave it there for $10$ full years when he will make a down payment on a car after graduation. How much of a down payment will he be able to make? $(7$ points$)$

$$

a$.$ $$25,057$

b$.$ $$29,450$

c$.$ $$31,241$

d$.$ $$33,856$

e$.$ None of the Above