1. A pension plan is obligated to make disbursements of $3.3 million, $4.0 million, and $3.3 million at the end of each of the next three years, respectively. Find the duration of the plan's obligations if the interest rate is 10% annually. (Do not round intermediate calculations. Round your answer to 4 decimal places.)

2.

You are managing a portfolio of $1.0 million. Your target duration is 27 years, and you can choose from two bonds: a zero-coupon bond with maturity five years and a perpetuity, each currently yielding 2%. Required:

a. How much of (i) the zero-coupon bond and (ii) the perpetuity will you hold in your portfolio? (Do not round intermediate calculations. Round your answers to 2 decimal places.)

zero-coupon bond: [ ] perpetuity bond:[ ] b. How will these fractions change next year if target duration is now twenty six years? (Do not round intermediate calculations. Round your answers to 2 decimal places.) zero-coupon bond: [ ] perpetuity bond:[ ]

3.

a. Find the duration of a 6% coupon bond making annual coupon payments if it has three years until maturity and a yield to maturity of 7.5%. (Do not round intermediate calculations. Round your answers to 4 decimal places.)

b. What is the duration if the yield to maturity is 11.5%? (Do not round intermediate calculations. Round your answers to 4 decimal places.)