Term

$1$ year

$2$ years

$3$ years

$5$ years

$7$ years

$10$ years

$20$ years

Rate$($EAR $\%)$

$2\mathrm{.}09$

$2\mathrm{.}36$

$2\mathrm{.}62$

$3\mathrm{.}28$

$3\mathrm{.}88$

$4\mathrm{.}13$

$5\mathrm{.}04$

a$.$ Calculate the present value of an investment that pays $ $5$ comma $000$ in two years and $ $2$ comma $000$ 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$5.)$

c$.$ Calculate the present value of receiving $ $2$ comma $800$ per$$ year, with$$ certainty, for the next $20$ years. Infer rates for the missing years using linear interpolation. $($Hint$$: Use a$$ spreadsheet.$)$