Question
Intro You bought a 10-year zero-coupon bond with a face value of $1,000 and a yield to maturity of 3.1% (EAR). You keep the bond for 5 years before selling it. Attempt 1/5 for 10 pts. Part 1 What was the price of the bond when you bought it? Part 2 What is the rate of return (HPR) if the yield to maturity is 4.9% when you sell the bond? Part 3 What is the rate of return (HPR) if the yield to maturity is 1.9% when you sell the bond?
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Answer to a math question Intro You bought a 10-year zero-coupon bond with a face value of $1,000 and a yield to maturity of 3.1% (EAR). You keep the bond for 5 years before selling it. Attempt 1/5 for 10 pts. Part 1 What was the price of the bond when you bought it? Part 2 What is the rate of return (HPR) if the yield to maturity is 4.9% when you sell the bond? Part 3 What is the rate of return (HPR) if the yield to maturity is 1.9% when you sell the bond?
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Part 1
To find the price of the bond when you bought it, we can use the present value formula for zero-coupon bonds:
PV = \frac{FV}{(1 + r)^n}
where PV is the present value, FV is the face value, r is the yield to maturity (as a decimal), and n is the number of years.
By substituting the given values into the formula, we can find the price of the bond:
PV=736.91
Answer: The price of the bond when you bought it was $736.91
Part 2
To find the rate of return (HPR) when the yield to maturity is 4.9%, we need to calculate the selling price of the bond and compare it to the price at which it was bought.
Using the present value formula again, this time with a new yield to maturity of 4.9%, we can find the selling price of the bond after holding it for 5 years:
PV=787.27
The rate of return (HPR) is then given by:
HPR = \frac{\text{Selling Price} - \text{Purchase Price}}{\text{Purchase Price}} \times 100
Substituting the values, we find:
HPR=\frac{787.27-736.91}{736.91\}
Answer: The rate of return (HPR) is approximately 6.83% when the yield to maturity is 4.9%.
To find the price of the bond when you bought it, we can use the present value formula for zero-coupon bonds:
where PV is the present value, FV is the face value, r is the yield to maturity (as a decimal), and n is the number of years.
By substituting the given values into the formula, we can find the price of the bond:
Answer: The price of the bond when you bought it was $736.91
Part 2
To find the rate of return (HPR) when the yield to maturity is 4.9%, we need to calculate the selling price of the bond and compare it to the price at which it was bought.
Using the present value formula again, this time with a new yield to maturity of 4.9%, we can find the selling price of the bond after holding it for 5 years:
The rate of return (HPR) is then given by:
Substituting the values, we find:
Answer: The rate of return (HPR) is approximately 6.83% when the yield to maturity is 4.9%.
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