Question $1,(7$ points$)$

The parents of a nine$-$year$-$old boy have agreed to deposit $$500$ in their son's bank account on his tenth birthday and to increase their deposit by $$50$ every year thereafter until his twentieth birthday. $($Using A$.$P or G$.$P techniques$)$

a$.$ How much will they have to deposit on his ${20}^{th}$ birthday?

b$.$ How much will they have deposited by his ${20}^{th}$ birthday?