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

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

b$.$ Calculate the present value of receiving $$800$ 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 $$2,300$ 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 $$5,000$ in $2$ years and $$4,000$ in $5$ years for certain.

The present value of an investment that pays $$5,000$ in $2$ years and $$4,000$ in $5$ years for certain is $$,($Round to the nearest cent.$)$

Data table

$($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$,\%),2\mathrm{.}08,2\mathrm{.}49,2\mathrm{.}65,3\mathrm{.}33,3\mathrm{.}79,4\mathrm{.}25,4\mathrm{.}99]]$