Math Problem Statement
A bond had a price of $1,946.05 at the beginning of the year and a price of $1,979.47 at the end of the year. The bond's par value is $2,000 and its coupon rate is 5.2 percent. What was the percentage return on the bond for the year?
Multiple Choice
5.25%
7.06%
7.53%
6.18%
1.69%
Solution
To calculate the bond’s percentage return for the year, we need to determine both the capital gain and the income from the bond. Here’s the step-by-step solution:
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Capital Gain: The capital gain is the difference between the ending and beginning prices.
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Coupon Payment: The bond’s coupon rate is 5.2%, so the annual coupon payment is calculated as follows:
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Total Dollar Return: This is the sum of the capital gain and the coupon payment.
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Percentage Return: To find the percentage return, divide the total dollar return by the beginning price and multiply by 100.
Answer:
The percentage return on the bond for the year is 7.06%.
Would you like further details on any step?
Here are some related questions:
- How does the coupon rate affect the bond’s yield?
- What is the difference between capital gain and coupon payment in bond returns?
- How would a change in the bond’s price impact the percentage return?
- What role does the par value play in determining the coupon payment?
- Why is the beginning price used as the base for calculating percentage return?
Tip: When evaluating bond returns, always consider both price appreciation (or depreciation) and coupon payments for an accurate yield.
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Math Problem Analysis
Mathematical Concepts
Finance
Percentage Return
Bond Yield
Formulas
Capital Gain = Ending Price - Beginning Price
Coupon Payment = Par Value × Coupon Rate
Total Dollar Return = Capital Gain + Coupon Payment
Percentage Return = (Total Dollar Return / Beginning Price) × 100
Theorems
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Suitable Grade Level
College-Level Finance or Advanced High School
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