A portfolio manager for a target retirement date bond mutual fund for clients with a 6-year investment holding horizon, would like to ensure a 5% annual compound return for the fund.He has a choice between two bonds.Whatever money he has to invest will be invested bonds of one type or the other, so the difference in the prices of the two types of bonds is not a consideration.

Find the Duration and Modified Duration for each bond (show your work and answer the questions below)

• Bond 1 has a 5% annual coupon rate, $1000 maturity value, n = 6 years, YTM = 5% (pays a $50 annual coupon at the end of each year for each of the 6 years and $1,000 maturity payment at the end of year 6).

• Bond 2 is a zero-coupon bond with a $1000 maturity value, and n = 6 years; YTM= 5%. (pays no coupons; only a $1,000 maturity payment at the end of year 6)

Suppose for the Coupon Bond 1 above, rates go down to 4% after you purchase the bond for the life of the bond.Thus, you have to invest each of your coupon payments at a 4% rate, and hold the bond to maturity, receiving your $1,000 maturity value at the end of year 6.