Math Problem Statement
A bond has a par value of $1,000, a current yield of 6.60 percent, and semiannual coupon payments. The bond is quoted at 97.27. What is the amount of each coupon payment?
Multiple Choice
$33.00
$66.00
$36.11
$32.10
$64.20
Solution
To determine the amount of each coupon payment, we can use the bond's current yield formula and the given information.
Given Data:
- Par Value: $1,000
- Current Yield: 6.60%
- Quoted Price: 97.27 (which means 97.27% of the par value)
- Coupon Frequency: Semiannual (twice a year)
Step 1: Find the Annual Coupon Payment
The current yield is calculated using the formula:
Rearranging for the Annual Coupon Payment:
Since the bond price is quoted at 97.27% of par, the Current Price is:
Thus:
Step 2: Find Each Semiannual Coupon Payment
Since the bond makes semiannual payments, each payment is half of the annual coupon:
Answer:
The amount of each coupon payment is $32.10.
Final Answer:
- $32.10
Would you like more details on bond calculations, or do you have any questions?
- How is the current yield related to bond pricing?
- Why does a bond's price differ from its par value?
- What factors impact the bond yield apart from the price?
- How does semiannual coupon frequency impact the bond payments?
- How do market interest rates affect bond prices and yields?
Tip: When dealing with bonds, remember that quoted prices are usually a percentage of par value.
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Math Problem Analysis
Mathematical Concepts
Bond Valuation
Yield Calculation
Semiannual Coupon Payments
Formulas
Current Yield = (Annual Coupon Payment) / (Current Price)
Annual Coupon Payment = Current Yield * Current Price
Semiannual Coupon Payment = Annual Coupon Payment / 2
Theorems
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Suitable Grade Level
College Level Finance or Advanced High School Economics
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