Answer:
The price of the bond today if the maturity time is in 30 years is $758.344481
The price of the bond rise if the time to maturity is 15 years is $795.6740653 .
The exact price difference between the 30 year and the 15 year bonds is -$37.3295843
As coupon rate is less than required return or market rate or yield to maturity, the price increases with decrease in time to maturity.
Explanation:
What is the price of the bond today if the time to maturity is 30 years?
price of the bond = 9%*1000/12%*(1-1/1.12^30)+1000/1.12^30
= $758.344481
Therefore, The price of the bond today if the maturity time is in 30 years is $758.344481
Does the price of the bond rise or fall if the time to maturity is 15 years?
price of the bond = 9%*1000/12%*(1-1/1.12^15)+1000/1.12^15
= $795.6740653
Therefore, The price of the bond rise if the time to maturity is 15 years is $795.6740653 .
What is the exact price difference between the 30 year and 15 year bonds?
exact price difference between the 30 year and the 15 year bond
= $758.344481 - $795.6740653
= -$37.3295843
Therefore, The exact price difference between the 30 year and the 15 year bonds is -$37.3295843
Explain the reason(s) for the change in price between the two maturities.
As coupon rate is less than required return or market rate or yield to maturity, the price increases with decrease in time to maturity.
