Answer:
A. Bond equivalent 10.82%
Effective annual yield to maturity of the bond 11.11%
B. Bond equivalent 10%
Effective annual yield to maturity of the bond 10.25%
C. Bond equivalent 9.49%
Effective annual yield to maturity of the bond 9.73%
Step-by-step explanation:
A. Calculation to Find the bond equivalent
We would determine the yield to maturity on a semi-annual basis using Financial Calculator which is:
N = 10*2 = 30
PV = -940
PMT = [10%/2]*1000 = 50
FV = 1000
Press CPT, then I/Y, which gives us 5.41%
Bond equivalent yield to maturity=5.41% × 2
Bond equivalent yield to maturity= 10.82%
Calculation to determine the Effective Annual Yield To Maturity of the bond
Effective annual yield to maturity = (1+.0541)^2– 1
Effective annual yield to maturity = (1.0541)^2– 1
Effective annual yield to maturity =1.1111 – 1
Effective annual yield to maturity = 0.1111 *100
Effective annual yield to maturity = 11.11%
Therefore the bond equivalent and effective annual yield to maturity of the bond will be:
Bond equivalent 10.82%
Effective annual yield to maturity of the bond 11.11%
b. Calculation to determine the bond equivalent
Based on the information given the bond is selling at par which therefore means that the yield to maturity on a semi annual basis will be the same as the semi annual coupon 5%.
Bond equivalent yield to maturity =5%*2
Bond equivalent yield to maturity= 10%.
Calculation to determine Effective annual yield to maturity
Effective annual yield to maturity = (1+.05)^2– 1
Effective annual yield to maturity = (1.05)^2– 1
Effective annual yield to maturity=1.1025-1
Effective annual yield to maturity=.1025*100
Effective annual yield to maturity =10.25%
Therefore the bond equivalent and effective annual yield to maturity of the bond will be:
Bond equivalent 10%
Effective annual yield to maturity of the bond 10.25%
c.Calculation to determine the bond equivalent
N = 10*2 = 30
PV = -1,040
PMT = [10%/2]*1000 = 50
FV = 1000
Bond equivalent yield to maturity=9.49%, or 4.75% on a semi-annual basis.
Calculation to determine the Effective Annual Yield To Maturity of the bond
Effective annual yield to maturity = (1+.0475)^2– 1
Effective annual yield to maturity = (1.0475)^2– 1
Effective annual yield to maturity =1.0973– 1
Effective annual yield to maturity = 0.0973*100
Effective annual yield to maturity = 9.73%
Therefore the bond equivalent and effective annual yield to maturity of the bond will be:
Bond equivalent 9.49%
Effective annual yield to maturity of the bond 9.73%