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: Current Yield=Annual Coupon PaymentCurrent Price\text{Current Yield} = \frac{\text{Annual Coupon Payment}}{\text{Current Price}}

Rearranging for the Annual Coupon Payment: Annual Coupon Payment=Current Yield×Current Price\text{Annual Coupon Payment} = \text{Current Yield} \times \text{Current Price}

Since the bond price is quoted at 97.27% of par, the Current Price is: Current Price=97.27%×1000=0.9727×1000=972.70\text{Current Price} = 97.27\% \times 1000 = 0.9727 \times 1000 = 972.70

Thus: Annual Coupon Payment=0.066×972.70=64.20\text{Annual Coupon Payment} = 0.066 \times 972.70 = 64.20

Step 2: Find Each Semiannual Coupon Payment

Since the bond makes semiannual payments, each payment is half of the annual coupon: Semiannual Coupon Payment=64.202=32.10\text{Semiannual Coupon Payment} = \frac{64.20}{2} = 32.10

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?


  1. How is the current yield related to bond pricing?
  2. Why does a bond's price differ from its par value?
  3. What factors impact the bond yield apart from the price?
  4. How does semiannual coupon frequency impact the bond payments?
  5. 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