The following information was available as of the close of business June 1, 2004 on government of Canada bonds.
Coupon...Maturity.....Price.....Yield
5.00%......June 1, 2005......102.35......2.60
10.50%......June 1, 2006......113.91......3.26
8.50%......June 1, 2007.....107.41......3.39
Calculate the anticipated one-year interest rate for 2006 (up to June 2007). (Round your answer to 2 decimal places.)
2006 - 2.93
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To calculate the anticipated one-year interest rate for 2006, we can use the yield-to-maturity (YTM) formula.
Yield-to-maturity (YTM) = (Coupon Payment + ((Face Value - Price) / Years to Maturity)) / ((Face Value + Price) / 2)
Let's calculate the YTM for the 10.50% bond, which matures on June 1, 2006:
Coupon Payment = 10.50% of Face Value = 0.105 * 100 = 10.50
Face Value = 100
Price = 113.91
Years to Maturity = 1
YTM = (10.50 + ((100 - 113.91) / 1)) / ((100 + 113.91) / 2)
YTM = (10.50 + (-13.91) / 1) / (213.91 / 2)
YTM = (10.50 - 13.91) / 106.955
YTM = -3.41 / 106.955
YTM = -0.0318 or -3.18%
The anticipated one-year interest rate for 2006 is -3.18% (rounded to 2 decimal places).
To calculate the anticipated one-year interest rate for 2006 (up to June 2007), you will need to use the information provided about the government of Canada bonds.
The interest rate (yield) of a bond is related to its price. As the price of a bond increases, its yield decreases and vice versa. Therefore, to calculate the anticipated one-year interest rate, you need to compare the prices of the bond with different maturities.
In this case, you have three bonds with different maturities: one maturing on June 1, 2005, another on June 1, 2006, and the last one on June 1, 2007. The bond maturing on June 1, 2006 can provide insight into the anticipated interest rate for that year.
Looking at the bond with the June 1, 2006 maturity, we can see that it has a price of 113.91. This means that the bond is trading at a premium or a price higher than its face value. A bond trading at a premium generally indicates a lower yield since investors are willing to pay more for the bond.
Given that the yield for the June 1, 2006 bond is 3.26%, this is the current interest rate associated with it. Therefore, the anticipated one-year interest rate for 2006 (up to June 2007) can be taken as 3.26%.
Hence, the anticipated one-year interest rate for 2006 is 3.26%.