a$.$ Calculate the present value of an investment that pays $$5,000$ in two years and $$3,000$ in five years for certain.

b$.$ Calculate the present value of receiving $$900$ per year, with certainty, at the end of the next five years. To find the

rates for the missing years in the table, linearly interpolate between the years for which you do know the rates. $($For

example, the rate in year $4$ would be the average rate in year $3$ and year $5.$