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

$12/31/2023).$ Kim's parents do not make

any more contributions.

Kim deposits $$5,500$ per year into the

same account while in college $($December

$31,2024$ until and including December

$31,2027).$ Immediately after making

that last deposit of $$5,500$ on December

$31,2027,$ 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 $31,2027$

$($immediately after making the last

$$5,500$ deposit$).$

What was the magnitude of the

equal, annual deposits made by

Kim's parents?