An insurance company has the liabilities with the following payment pattern, each at the end of the respective year:

Year 3: $2.5 million

Year 7: $4.2 million

Year 20: $6.0 million

There are no other liabilities for the insurance company to consider. The discount rate for the liabilities is 3%. The insurance company has the following investment opportunities in bonds and stocks:

Coupon Bonds

Maturity	Yield	Duration
4	7.0%	3
10	9.0%	7
20	10.0%	11
30	11.0%	20

Common stocks

Stock	Dividend	Duration
A	5.0%	20
B	9.3%	11
C	10.0%	10
D	14.3%	7

Zero Coupon Bonds

Maturity	Yield
3	1.5%
5	2.0%
7	2.0%
10	3.0%
15	3.5%

a. Using the information about the zero-coupon bonds, draw the yield curve and compute two forward rates of your choice.

b. Calculate the duration of the liability.