10-17I
Expert-verifiedA 20-year maturity bond with par value $1,000 makes semiannual coupon payments at a coupon rate of 8%. Find the bond equivalent and effective annual yield to maturity of the bond if the bond price is:
a. $950
b. $1,000
c. $1,050
a. When the bond price is $950, the bond equivalent is 8.52% and the effective annual yield to maturity is 8.70%
b. When the bond price is $1000, the bond equivalent is 8% and the effective annual yield to maturity is 8.16%
c. When the bond price is $1050, the bond equivalent 3.76% and the effective annual yield to maturity is 7.66%
Available inputs: n = 40, FV = 1000, PV = –950, PMT = 40.
The yield to maturity on a semi-annual basis =
Yield To Maturity = (Face Value/Current Bond Price)^(1/Years To Maturity)−1
= (1000 / -950) )^(1/40)−1
= 4.26%.
This implies a bond equivalent yield to maturity of: 4.26% x 2 = 8.52%
Effective annual yield to maturity i = [1 + (r/n)]^{n} – 1
(1.0426)^{2} – 1 = 0.0870 = 8.70%
b. Since the bond is selling at par, the yield to maturity on a semi-annual basis is the same as the semi-annual coupon, 4%.
The bond equivalent yield to maturity is 8%.
Effective annual yield to maturity i = [1 + (r/n)]^{n} – 1
= (1.04)^{2} – 1 = 0.0816 = 8.16%
Available inputs: n = 40, FV = 1000, PV = –1050, PMT = 40.
The yield to maturity on a semi-annual basis =
Yield To Maturity = (Face Value/Current Bond Price)^(1/Years To Maturity)−1
= (1000 / -1050) )^(1/40)−1
= 7.52%.
This implies a bond equivalent yield to maturity semi-annually: 7.52% / 2 = 3.76%
Effective annual yield to maturity i = [1 + (r/n)]^{n} – 1
(1.0376)^{2} – 1 = 0.0766 = 7.66%
Question: The following table contains spot rates and forward rates for three years. However, the labels got mixed up. Can you identify which row of the interest rates represents spot rates and which one the forward rates?
Year | 1 | 2 | 3 | |
Spot rate of Forward rates? | 10.00% | 12.00% | 14.00% | |
Spot rate of Forward rates? | 10.00% | 14.0364% | 18.1078% |
94% of StudySmarter users get better grades.
Sign up for free