Assume the current Treasury yield curve shows that the spot rates for six months, one year, and one and a half years are 1 %1%, 1.1 %1.1%, and 1.3 %1.3%, all quoted as semiannually compounded APRs. What is the price of a $1 comma 0001,000 par, 4.25 %4.25% coupon bond maturing in one and a half years (the next coupon is exactly six months from now)? The price of this bond is $nothing.

Answer:

present value of bond = $1042.96

Explanation:

given data

spot rates for six months = 1%

spot rates for one and = 1.1%

spot rates for one and half years = 1.3%

price = $1000

coupon bond = 4.25%

time = 6 month

solution

we get here first price on bond paid that is

coupon paid = $1000 × 4.25 × 0.5 = $21.25

we get here present value of 6 month and 1 year and 1 and half year

present value = $\frac{coupon\ payment }{(1+\frac{spot \ rate}{2})^t}$ ..............1

present value of 6 month = $\frac{21.25}{(1+\frac{0.1}{2})^1}$ = 20.23

present value of 1 year = $\frac{21.25}{(1+\frac{0.011}{2})^2}$ = 21.01

present value of 1 year and half year = $\frac{21.25}{(1+\frac{0.013}{2})^2}$ = 20.97

and

now we get present value of par value in 1 and half year

present value of par value in 1 and half year = $\frac{par\ value}{(1+\frac{spot rate}{2})^3}$

present value of par value in 1 and half year = $\frac{1000}{(1+\frac{0.013}{2})^3}$

present value of par value in 1 and half year = 980.75

present value of bond will be as

present value of bond = 20.23 + 21.01 + 20.97 + 980.75

present value of bond = $1042.96

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