Assume you can earn $9\%$ on the investments described below. How much money would each investment provide for you after six$$ years?

a$.$ Invest $$$$4,200$ as a lump sum today.

b$.$ Invest $$$$1,610$ at the end of each of the next $6$ years.

c$.$ Invest a lump sum of $$$$2,390$ today and $$$$842$ at the end of each of the next $6$ years.

d$.$ Invest $$$$768$ at the end of years$1,3,$ and $5.$