Question

A newly issued U.S. Federal? T-Note matures in exactly 7 years. The coupon rate is 3.875?% per year and coupons are paid semiannually. The bond is priced at 102.31 ?(per $100 of face? value) and yields 3.50?%. The economy is slowing and many forecasters predict a recession. You expect that the monetary authorities will relax monetary policy which will cause interest rates to fall. You expect the yield on the 7?-year bond to fall to 2.50?%. The bond has a face value of? $1M. If you want to earn? $1M by investing in bonds to profit from the interest rate? change, how many bonds do you? buy???

In order to earn? $1M by investing in? bonds, you need to buy _____bonds.???(Round up to the nearest whole? number.)

Answer 1

Price of the bond per 100 of face value, before fall in yield=102.31
Price of the bond per 100 of face value, after fall in yield=(3.875%/2*100)/(2.5%/2)*(1-1/(1+2.5%/2)^(2*7))+100/(1+2.5%/2)^(2*7)=108.779755

Profit per 100 of face=(108.779755-102.31)=6.469755
Profit per 1 of face=(108.779755-102.31)=0.06469755

TO earn, $1 million, face value needed=1000000/0.06469755=15456535.83
Or, number of bonds with face value 1 million needed=15456535.83/1000000=15.45653583

or 16 bonds