$4\mathrm{.}2\mathrm{.}6$ Kayla receives a $$6,000$ high school graduation present which she puts in a savings account paying $4\mathrm{.}15\%$ annual interest, compounded monthly $($see Exercise $4\mathrm{.}2\mathrm{.}5).$ She plans to work for two years before starting college, put her earnings in the account, and then live off the money in the account during college. Here are the details of her plan:

She will deposit the same amount into the account at the end of each month for the two years she works $($starting in month $1).$

In month $25$ she will stop making deposits and start withdrawing $$1,000$ each month for her first year in college.

During her second year she will withdraw $$1,250$ each month. During her third and fourth years she will withdraw $$1,500$ and $$1,750$ each month, respectively.

Figure out how much she must deposit each month for the first two years so she has $$0$ left in the account at the end of her fourth year of college. Approximately how much tota interest does she earn over the six years?