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Mr
Mr. Bean buys two bonds. One bond is bought to yield 4% effective annually and is a three-year Zero-coupon bond that can be redeemed for 1000. The second bond is a 1000 par value 6% semiannual coupon bond that matures in 6 years. If, both bonds have the same price, calculate the effective yield on the coupon bond.
Expert Solution
We can calculate the price of one bond by using the following formula in excel:-
=-pv(rate,nper,pmt,fv)
Here,
PV = Price of one bond
Rate = 4%
Nper = 3 periods
Pmt = 0
FV = 1000
Substituting the values in formula:
= -pv(4%,3,0,1000)
= 889
We can calculate the rate on second bond by using the following formula in excel:-
=rate(nper,pmt,-pv,fv)
Here,
Rate = Rate on second bond (semiannual)
Nper = 6*2 = 12 periods (semiannual)
Pmt = Coupon payment = 1000*6%/2 = 30
PV = 889
FV = 1000
Substituting the values in formula:
= rate(12,30,-889,1000)
= 4.20%
Effective yield = (1+Semi annual yield)^n-1
= (1+4.20%)^2-1
= 1.0857 - 1
= 8.57%
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