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Dmytriw buys a bond with 25 years until maturity
Dmytriw buys a bond with 25 years until maturity. The face value is $1000 and the coupon rate is 4%. a) If the current interest rate is 8.35% compounded 4 times per year, what is the price of the bond? b) If Dmytriw insists on earning at least 9.75%, what price should he be willing to pay for the bond? c) If Tanya pays $10 more than what Dmytriw paid in part b), what interest rate is she earning on her investment?
Expert Solution
a)Computation of Price of Bond using PV Function in Excel:
=-pv(rate,nper,pmt,fv)
Here,
PV = Price of Bond = ?
Rate = 8.35%/4 = 2.0875%
Nper = 25 Years * 4 = 100 Periods
PMT = $1,000*4%/4 = $10
FV = $1,000
Substituting the values in formula:
=-pv(2.0875%,100,10,1000)
PV or Price of Bond = $545.04
b)Computation of Price of Bond using PV Function in Excel:
=-pv(rate,nper,pmt,fv)
Here,
PV = Price of Bond = ?
Rate = 9.75%/4 = 2.4375%
Nper = 25 Years * 4 = 100 Periods
PMT = $1,000*4%/4 = $10
FV = $1,000
Substituting the values in formula:
=-pv(2.4375%,100,10,1000)
PV or Price of Bond = $463.32
c) Computation of Interest Rate using Rate Function in Excel:
=rate(nper,pmt,-pv,fv)
Here,
Rate = Interest Rate = ?
Nper = 25 Years
PMT = $1,000*4% = $40
PV = $463.32+$10 = $473.72
FV = $1,000
Substituting the values in formula:
=rate(25,40,-473.32,1000)
Rate or Interest Rate = 9.64%
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