Joe has pension plan that will pay him $20,000 annually over the course of 10 years. He will receive his first payment in five years, and the fund is looking to immunize its position.

a) What is the duration of this fund's obligation to Joe if the current interest rate is 9%?

b) If the pension plan will pay Joe $20,000 a year infinitely, instead of over 10 years, what is the duration? The first payment will also be received in five years.