Assume you must invest $100,000, and bonds given below from A to E are only investments available today. Suppose that it is potential to buy the fraction of the bond in order to invest complete amount of $100,000 (like it is probable to buy 142.58 of bond C). Same 6% market interest rate (APR, compounded semi-annually) relevant to all of these bonds and they have the extra characteristics given below:

A) 6 years to maturity and 4% coupon rate (coupons paid annually)
B) 3 years to maturity and 7% coupon rate (coupons paid semi-annually)
C) 6 years to maturity and 0% coupon rate (discount or zero-coupon bond)
D) 3 years to maturity and 4% coupon rate (coupons paid semi-annually)
E) 6 years to maturity and 4% coupon rate (coupons paid semi-annually)

problems:

i) Grade these bonds according to their interest rate sensitivities, from most interest rate sensitive to the least interest rate sensitive.

ii) If you desire to benefit from the unexpected decrease in market interest rates, which bond would you purchase?

iii) If you wish to minimize interest rate risk, which bond must you purchase?

iv) Find the duration (in years) of bond you selected in part iii)?