$($a$)$ For a $30-$year, $6\%$ coupon, semi annual payments, face value $$1000,$ if the yield is $8\%,$ compute the current bond price.

N $=30*2=60$

I$/$Y $=8\%/2=4\%$

PMT $=(1000*0\mathrm{.}06)/2=30$

FV $=1000$

PV $=???=773\mathrm{.}77$

$($b$)$ Two years later, if the yield of the same bond becomes $9\%,$ compute the new bond price then.

N $=28*2=56$

I$/$Y $=9\%/2=4\mathrm{.}5\%$

PMT $=(1000*0\mathrm{.}06)/2=30$

FV $=1000$

PV $=???=695\mathrm{.}00$

$($c$)$ If to buy at $($a$)$ price and sell at $($b$)$ price, compute the realized $($horizon$)$ return on this bond investment.

N $=2*2=4$

I$/$Y $=???=1\mathrm{.}38436*2=2\mathrm{.}77\%$

PMT $=(1000*0\mathrm{.}06)/2=30$

FV $=695$

PV $=-773\mathrm{.}77$

$(695/773\mathrm{.}77)-1*100=-10\mathrm{.}18\%$

On $($c$),$ how do I know when to put the number in my calculator versus the formula we used above?