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1)A 10 year bond which has just been issued, provides semiannual coupons of 6% a year in arrears
1)A 10 year bond which has just been issued, provides semiannual coupons of 6% a year in arrears. It is redeemed at par. What price is paid (per $100 nominal value) if bond yields an annual effective rate of interest of 8%? Ans: $87.37 2. A 20-year zero-coupon bond is redeemed at par. If the price paid per $1,000 face amount is $538.76, determine the annual effective yield rate. Ans: 3.14% 3. A bond pays semi-annual coupons at an annual rate of 10% of the nominal value. The annual effective yield to maturity is currently 4%, and the price paid per $1,000 par value is $1,404.06. If the bond is redeemed after 7 years, calculate the redemption payment. Ans: $1,050.00 4. An n-year bond pays annual coupons of 5% semiannually. The annual effective yield is 8% and the price per $100 par value is $86. The bond is redeemed at 110%. Find n. Ans: 10.
Expert Solution
1. Par Value =100
Semi annual Coupon =Coupon Rate*Par value/2 =6%*100/2 =3
Number of periods(n) =10*2 =20
Semi Annual Rate =(1+Effective Rate)^0.5-1 =(1+8%)^0.5-1 =3.923%
Price of Bond =semi annual Coupon*((1-(1+rate)^-n)/r)+Par Value/(1+r)^n
=3*((1-(1+3.923%)^-20)/3.923%)+100/(1+3.923%)^20 =87.37
2. Price of Bond =538.96
Number of Years =20
Par Value =1000
Annual Effective yield Rate =(Par Value/Price)^(1/n)-1 =(1000/538.96)^(1/20)-1 =3.14%
3. Par Value =1000
Semi annual Coupon =Coupon Rate*Par value/2 =10%*1000/2 =50
Number of periods(n) =7*2 =14
Semi Annual Rate =(1+Effective Rate)^0.5-1 =(1+4%)^0.5-1 =1.9803903%
Price of Bond =semi annual Coupon*((1-(1+rate)^-n)/r)+Redemption Payment/(1+r)^n
1404.06=50*((1-(1+1.9803903%)^-14)/1.9803903%)+Redemption Payment/(1+1.9803903%)^14
1404.06 =606.1487+Redemption Payment/(1+1.9803903%)^14
Redemption Payment =(1404.06-606.1487)*(1+1.9803903%)^14 =1050
4. Par value =100
Price =86
Redemption value =110%*Par value =110%*100 =110
Semi Annual Rate =(1+Effective Rate)^0.5-1 =(1+8%)^0.5-1 =3.92304845413265%
Semi Annual Coupon =5%*Par Value/2 =5%*100/2 =2.5
Calculating Number of Period using financial Calculator
I/Y =3.92304845413265%;PMT =2.5;PV=-85;FV=110;CPT N =20.19
Number of Years 2=20.19/2 =10.095 or 10 years
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