4. (Zero Coupon Bonds) A zero coupon bond is a debt security that does not pay interest but trades

at a discount, and will pay its face value at maturity. Suppose a zero coupon bond matures to a

value of $1000 in eight years. If the bond is yielding at 4% per annum, what is the purchase price of

the bond? Suppose a 8-year coupon-paying bond is paying $40 a year, and has a face value of $1000

is selling for $1000. What is the bond yield of the coupon-paying bond? Should you be indifferent in

holding the two bonds given the same yield, if you intend to hold the bond to maturity?

5. Peter plans to retire 33 years from now. He expects that he would live 27 years after retiring, and

would want to have enough money upon reaching retirement age to withdraw $180,000 from the

account at the beginning of each year he expects to live, and yet still have $2,500,000 left in the

account at the time of his expected death (60 years from now). Peter plans to accumulate the

retirement fund by making equal annual deposits at the end of each year for the next 33 years. He

expects that he can earn 12% per year on his deposits. However, he only expects to earn 6% per

year on his investment after he retires. What equal annual deposits must he make each year to

reach his retirement goal?

Answers:

4. $730.7; 4% yield for coupon-paying bond.

5. $8874.8

Could you please show me the process? Thank you