Suppose the term structure of risk$-$free interest rates is as shown here: $.$

a$.$ Calculate the present value of an investment that pays $$1,000$ in $2$ years and $$4,000$ in $5$ years for certain.

b$.$ Calculate the present value of receiving $$900$ per year, with certainty, at the end of the next $5$ 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 $5.)$

c$.$ Calculate the present value of receiving $$2,700$ per year, with certainty, for the next $20$ years. Infer rates for the missing years using linear interpolation. $($Hint: Use a spreadsheet.$)$