Assume the following yield curve for zero-coupon bonds:

Maturity Yield

1 year 5%

2 years 6%

3 years 7%

4 years 8%

5 years 9%

a) What is Macaulays duration of each of the bonds?

b) Assume that your investment horizon is 3 years and you want to buy bonds with 1- and 4- year maturities. What percentage investment should be made in each bond to assure

a fully immunized portfolio?

please no excel ,show full answer