Question $8,$ Problem $5-31($bookmatch$)$

HW Score: $66\mathrm{.}67\%,8$ of $12$ points

Part $2$ of $2$

Points: $0$ of $1$

Suppose the term structure of risk$-$free interest rates is shown below.

$\backslash$table$[[$Term$,1$ year,$2$ years,$3$ years,$5$ years,$7$ years,$10$ years,$20$ years$],[$Rate $($EAR$,\%),1\mathrm{.}99,2\mathrm{.}41,2\mathrm{.}74,3\mathrm{.}32,3\mathrm{.}76,4\mathrm{.}13,4\mathrm{.}93]]$

What is the present value of an investment that pays $$100$ at the end of each of years $1,2,$ and $3?$ If you wanted to value this investment correctly using the annuity formula, which discount rate should you use?

The present value of the investment is $$286\mathrm{.}16.$

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

To value this investment correctly using the annuity formula, use the discount rate $\%.$

$($Round to five decimal places.$)$