Jack has recently acquired a new boat and wishes to financially prepare

for its maintenance over the initial eight years. Based on advice from her

boat dealer, the maintenance cost projections are as follows:

$$ Year $1$: No maintenance expenses.

$$ Year $2$: Maintenance cost of $$200.$

$$ From Year $3$ onwards: An annual increment of $$50$ to the maintenance

cost $($e$.$g$.,$ $$250$ in Year $3,$ $$300$ in Year $4,$ etc.$).$

In order to meet these expenses, Jack intends to make a one$-$time deposit

into a savings account that offers an $8\%$ annual interest rate, compounded

yearly. Determine the lump sum amount Jack should deposit to ensure she

can cover the anticipated maintenance expenses over the eight$-$year period