$1.$ Consider a pure$-$discount bond that matures in exactly $12$ years and pays $$1,000$ at maturity.

$($a$)$ What is the value of the bond if the discount rate is $6\%?$

$($b$)$ What is the value of the bond if the discount rate is $12\%?$

$($c$)$ Assuming the bond is priced at the value you calculated in $($b$),$ what is the bond$$s yield$-$to$-$ maturity?

$*$If this could be explained in excel that would be awesome, I truly want to understand how to do this$*$