Please answer C and show your work! Thank you. Suppose the term structure of risk$-$free interest rates is as shown here:

a$.$ Calculate the present value of an investment that pays $\backslash (\backslash$$ $2,500\backslash )$ in $2$ years and $\backslash (\backslash$$ $2,000\backslash )$ in $5$ years for certain.

b$.$ Calculate the present value of receiving $\backslash (\backslash$$ $300\backslash )$ 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 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 $\backslash (\backslash$$ $2,600\backslash )$ 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 $\backslash (\backslash$$ $2,500\backslash )$ in $2$ years and $\backslash (\backslash$$ $2,000\backslash )$ in $5$ years for certain.

The present value of an investment that pays $\backslash (\backslash$$ $2,500\backslash )$ in $2$ years and $\backslash (\backslash$$ $2,000\backslash )$ in $5$ years for certain is $\backslash (\backslash$$ $4085\mathrm{.}93\backslash ).($Round to the nearest cent.$)$

b$.$ Calculate the present value of receiving $\backslash (\backslash$$ $300\backslash )$ 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 do know the rates. $($For example, the rate in year $4$ would be the average rate in year $3$ and year $5.)$

The present value of receiving $\backslash (\backslash$$ $300\backslash )$ per year, with certainty, at the end of the next $5$ years is $\backslash (\backslash$$ $1380\mathrm{.}44\backslash ).($Round to the nearest cent.$)$

c$.$ Calculate the present value of receiving $\backslash (\backslash$$ $2,600\backslash )$ per year, with certainty, for the next $20$ years. Infer rates for the missing years using linear interpolation. $($Hint: Use a spreadsheet.$)$

The present value of receiving $\backslash (\backslash$$ $2,600\backslash )$ per year, with certainty, for the next $20$ years is $\backslash (\backslash$$ $\backslash$square $\backslash ).($Round to the nearest cent.$)$

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