Firm A issues a zero-coupon bond with a face value of $100,000 at

the beginning of the first year (t=0) which is purchased by investor B. The

bond matures at the end of 20 years (t=20). The prevailing interest rate at

t=0 for bonds with similar risk is 5%.

Consider the following for Investor B:

(a) How much does Investor B pay for this 20-year $100,000 zero-coupon bond

at t=0? What is the yield to maturity?

(b) Suppose that when markets open on the first day of the sixth year, the

interest rate is still 5%. What would be the price of the bond that

morning?

(c) Suppose that by the time the markets close on the first day of the sixth

year, interest rates have fallen to 4%. What would be the price of

Investor B's bond at the end of the day? (For calculations, ignore the

fact that one day has passed, just assume we are still at the beginning

of the sixth year).

(d) Suppose Investor C buys Investor B's bond at the beginning of the ninth

year for $60,000. Assuming this was a fair exchange, what does this tell

you about the movement of interest rates between the beginning of the

sixth year and the beginning of the ninth year?

(e) Redo (b) and (c) in the case that the bond that Firm A issued at

t=0 was

actually a 30-year bond rather than a 20-year bond. What does your answer

tell you about the relationship between time to maturity and price

volatility?

Problem 2:

Prove mathematically that for a level coupon bond, the discount

rate equals to the coupon rate, if the bond price is the face value.