Question

What is the price of the following US T-Bond? (Use any method you prefer, and enter your answer with two decimal places)

Face value : $100

Maturity: 6 years

Coupon rate 3% (paid annually)

Yield = 7.6%

Suppose you observe that the above bond is trading at $83.00. What is the yield? (Enter your answer as a percentage with the % sign, with two decimal places)

Calculate the price, duration, and modified duration of this bond when the yield is 9% (Enter all answers with two decimal places).

Answer 1

Answer: we will compute the value using financial calculator

FV = $100

N = 6

PMT = $3 (coverted coupon rate to dollar amount)

I/Y = 7.6%

PV = $78.47

Price of the bond = $78.47

Part 2 -

FV = $100

N = 6

PMT = $3 (coverted coupon rate to dollar amount)

PV = $83

I/Y = 6.51%

Part 3 -

FV = $100

N = 6

PMT = $3 (coverted coupon rate to dollar amount)

I/Y = 9%

Price of the bond = $73.08

Duration of the bond = Present value of the cash flows/ Price of the bond

PV calculation

Duration = 401.4953/73.08

Duration = 5.49

Modified Duration = Duration/ (1+ YTM/n)

Modified Duration = 5.49/(1+9%/6)

Modified Duration = 5.49/(1+1.5%) or 5.49/(1+0.015)

Modified Duration = 5.41