$1.$ Use the following equation to find the future value of a $$30,000$ investment into a $20$ year treasury at $2\mathrm{.}64\%?$ Assume this investment only compounds at a rate of once per year. Also assume we are given the nominal rate of interest.

$FV=PV(1+r{)}^n$

$2.$ Lets assume the rate of inflation is represented by the target average of roughly $2\mathrm{.}5\%.$Using the same inputs, what is the real return of our $20$ year treasury? Show all your work.

$3.$ We now want to pursue a more short term investment with more liquidity. Currently, the yield on $2-$year US treasuries is $2\mathrm{.}51\%.$ Our $2-$year treasury will yield a coupon payment every $6-$months. Given the expanded version of our FV equation, what is the future value of this investment if all coupon payments were re$-$invested into principal until maturity? Note: we are only finding nominal returns here.

$FV=PV(1+\frac{r}{t}{)}^{(n)(t)}$

$4.$ We would now like to know the present value of our $10-$year treasury from question one. Use your result from question $1$ for $FV,$ this time we'll assume a typical compounding period for bonds of every $6$ months $($remember we are discounting$).$ Use the present value form of our equation presented below:

$PV=\frac{FV}{(1+\frac{r}{t}{)}^{(n)(t)}}$