The six-year spot rate is 7% and the five-year spot rate is 6%. What is the implied one-year zerocoupon bond rate five years from now?
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A. B. C. D.D
5r1= [(1 +/ (1 +] - 1 = [(1.07/(1.06] "" 1[1.5 / 1.338] - 1 = .12
To calculate the implied one-year zero-coupon bond rate five years from now, we can use the concept of bootstrapping. Bootstrapping is a method used to derive the implied spot rates for different maturities based on observed spot rates.
In this case, we have the six-year spot rate as 7% and the five-year spot rate as 6%. The six-year spot rate represents the interest rate for a six-year zero-coupon bond, while the five-year spot rate represents the interest rate for a five-year zero-coupon bond.
To calculate the implied one-year zero-coupon bond rate five years from now, we need to determine the spot rate for a one-year bond maturing in five years. We can achieve this by using the concept of forward rates.
The forward rate is the implied interest rate on a future investment period, given the current spot rates. In this case, we want to find the forward rate for the one-year period starting five years from now.
We can calculate the forward rate using the formula:
(1 + Spot rate for the one-year bond)^1 = (1 + Spot rate for the five-year bond)^5 * (1 + Forward rate)^1
Let's denote the forward rate as "x" for simplicity. Plugging in the given spot rates:
(1 + x)^1 = (1 + 0.06)^5 * (1 + 0.07)^1
Simplifying the equation:
1 + x = (1.338225) * (1.07)
1 + x = 1.43087675
x = 1.43087675 - 1
x = 0.43087675
Therefore, the implied one-year zero-coupon bond rate five years from now is approximately 0.4309 or 43.09%.
Since the available answer choices are given in percentages, we can round it to the nearest percentage, which is 43%. However, none of the given answer choices matches this value, so it seems that there might be an error in the answer choices provided.