A girl$$s parents wish to save money for her college education starting at birth. The girl$$s grandparents offered an initial investment of $$5000$ right at the moment she is born $($i$.$e$.$ in Year $0).$ Tuition costs are expected to be $$40,000$ per year in the $18$th$,19$th$,20$th$,$ and $21$st years of the girl$$s life. The parents are able to invest $$2000$ a year for $5$ years, starting on the $5$th year of her life $($years $5,6,7,8,9,$ and $10).$ Starting in year $11,$ they will be able to increase their investment amounts by a flat amount each year $($so each year will have a flat amount more than the last year for years $9$ through $17).$ The parents will stop investing money after year $17.$ How much will the family have to increase their contributions in order to make the tuition payments? Assume a $5\%$ interest rate. Draw the cash flow diagram to help you visualize the cash flows.

$$ Ans: $$3064\mathrm{.}19$