Please Show Work Step By Step, NO Excel. Thank you!

Duke Power plans to issue $100 million of bonds. It needs one month to prepare the documentation. It is concerned that interest rates might rise before it can sell the issue. its current new-issue rate is 9% for 30 year bonds.

b) the yield on 8% 20 year Treasury bonds is 7.5%. The yield on these bonds will rise to 8.5% if Duke's borrowing cost rises to 10%. Calculate the hedge ratio.

at 9% the price of Duke's bonds is $100

at 10% the price of Duke's bonds is:

answers: n = 60 r=5% pmt = $4.5 fv =100 --> Pv = -$90.54

how did he get pmt = $4.5 and fv=100?

how do you input this in the calculator step by step?

at 7.5% the price of the T-bonds is:

n=40 r=3.75% pmt=$4 fv=$100 --> Pv= -$105.14

why is n=40?

at 8.5% the price of the t-bonds is:

n=40 r=4.25% pmt= $4 fv=$100 --> Pv= -$95.23