Find the yield to maturity of a zero coupon bond with 1,000 par that matures in 7 years and is currently selling for $550

Finance Oct 23, 2020

Find the yield to maturity of a zero coupon bond with 1,000 par that matures in 7 years and is currently selling for $550. (Hint: the conventional method of pricing zero-coupon bonds is to use semi-annual compounding to find the YTM)

Expert Solution

Current selling price=PV of the cash flows of the bond , ie. Face value at end of 7 yrs, ie. 7*2=14 semi-annual periods,

at semi-annual compounding rate of interest, r

ie. 550=1000/(1+r)^14

solving for r, we get the semi-annual r as

(1+r)^14=1000/550

1+r=(1000/550)^(1/14)

r=(1000/550)^(1/14)-1=

0.043628

Now, the annual r, ie. YTM =

(1+0.043628)^2-1=

8.92%

(YTM) --Answer

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