Kim is a first$-$year student in college. On

December $31,2005,$ Kim's parents opened a

savings account for her with an $8\%$ interest

rate and put an equal amount of money in it

every year until $($and including$)$ December

$31,2023($first deposit is $12/31/2005$ and

last deposit is $\frac{12}{31}\frac{?}{2023}).$ Kim's parents

do not make any more contributions.

Kim deposits $$6,500$ per year into the same

account while in college $($December $31,2024$

until and including December $31,2028).$

Immediately after making that last deposit of

$$6,500$ on December $31,2028,$ Kim has a

bank balance is $$150,000.$

Draw a cash flow diagram from the

bank's point of view assuming Kim

withdraws the entire $$150,000$

balance on December $31,2028$

$($immediately after making the last

$$6,500$ deposit$).$

What was the magnitude of the equal,

annual deposits made by Kim's

parents?