Suppose the term structure of risk$-$free interest rates is as shown below: $($Click on the following icon $$ in order to copy its contents into a spreadsheet.$)$

$\backslash$table$[[$Term$,1$ year,$2$ years,$3$ years,$5$ years,$7$ years,$10$ years,$20$ years$],[$Rate $($EAR $\%),1\mathrm{.}93,2\mathrm{.}34,2\mathrm{.}64,3\mathrm{.}34,3\mathrm{.}81,4\mathrm{.}22,5\mathrm{.}08]]$

a$.$ Calculate the present value of an investment that pays $$2,500$ in two years and $$4,000$ in five years for certain. b$.$ Calculate the present value of receiving $$500$ 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 $5.)$

c$.$ Calculate the present value of receiving $$2,400$ per year, with certainty, for the next $20$ years. Infer rates for the missing years using linear interpolation. $($Hint: Use a spreadsheet.$)$

a$.$ Calculate the present value of an investment that pays $$2,500$ in two years and $$4,000$ in five years for certain.

The present value of the investment is $

$($Round to the nearest cent.$)$