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Suppose a? 10-year, $1,000 bond with an 8
Suppose a? 10-year, $1,000 bond with an 8.7% coupon rate and? semi-annual coupons is trading for a price of ?$1,034.58.
a) What is the? bond's yield to maturity? (expressed as an APR with? semi-annual compounding)?
b) If the? bond's yield to maturity changes to 9.3% ?APR, what will the? bond's price? be?
Expert Solution
a) We can calculate the yield to maturity by using the following formula in excel:-
=rate(nper,pmt,-pv,fv)
Here,
Rate = Yield to maturity (semiannual)
Nper = 10*2 = 20 periods (semiannual)
Pmt = Coupon payment = $1,000*8.7%/2 = $43.50
PV = $1,034.58
FV = $1,000
Substituting the values in formula:
= rate(20,43.50,-1034.58,1000)
= 4.09%
Yield to maturity = Rate * 2
= 4.09% * 2
= 8.19%
b) We can calculate the bond price by using the following formula in excel:-
=r-pv(rate,nper,pmt,fv)
Here,
PV = Bond price
Rate = 9.3%/2 = 4.65% (semiannual)
Nper = 10*2 = 20 periods (semiannual)
Pmt = Coupon payment = $1,000*8.7%/2 = $43.50
FV = $1,000
Substituting the values in formula:
= -pv(4.65%,20,43.50,1000)
= $961.48
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