# Price a sequence of zero rates

Suppose you have the price a sequence of zero rates

Maturity (Yrs) Zero rates (Continuous compounding)

0.5 5.20%

1 5.30%

1.5 5.30%

2 5.45%

(a) If convert Zero rates to compound 12 times per annual, what is their value?

(b) What is the zero rate for year 2.5 if a bond has coupon rate=9%, price = $108.15, maturity =2.5? (Semiannually ex-coupon, continuous compounding)

(c) Calculate and fill in the table below. (Semiannually pay coupon, continuous compounding, Face value=100)

(first column of numbers given is Year; second column of numbers given is

Annual Coupon %; find Discount Factor, Forward Rate, Bond Price, YTM, Par Yield for each given Year and Annual Coupon %)

Year Discount Forward Annual Bond YTM* Par

Factor Rate Coupon(%) Price($) Yield

---------------------------------------------------------------

0.5 0%

1 5%

1.5 7%

2 8%

YTM* := Yield to Maturity (or bond yield)

(d) If there is an opportunity that you could lend (or borrow) money to (from) somebody at year 1 for one year charging 5.30% what would you do?

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Suppose you have the price a sequence of zero rates

Maturity (Yrs) Zero Rate (Continuous compounding)

0.50 5.20%

1.00 5.30%

1.50 5.30%

2.00 5.45%

(a) If convert Zero rates to compound 12 times per annual, what is their value?

Maturity (Yrs) Zero Rate (Coumpound 12 times per year)

0.50 5.2113%

1.00 5.3117%

1.50 5.3117%

2.00 5.4624%

(b) What is the zero rate for year 2.5 if a bond has coupon rate=9%, price = $108.15, maturity =2.5? (Semiannually ...

#### Solution Summary

The solution discusses the price of a sequence of zero rates.