A newly issued bond has the following characteristics:

Par value = $1000

Coupon rate = 8%

Yield to Maturity = 8%

Time to maturity = 15 years

Duration = 10 years

1. Calculate modified duration using the information above.

2. If the yield to maturity increases to 8.5%, what will be the change (in dollar amount) in bond price?

3. Identify the direction of change in modified duration if:

i. the coupon of the bond is 4%, not 8%.

ii. the maturity of the bond is 7 years, not 15 years.

4. How can you construct a portfolio with a duration of 8 years using this bond and a 5 year zero coupon bond?