Math Problem Statement

A bond with a par value of 1000 is bought to yield 7.6% convertible semi-annually. The bond pays semi-annual coupons at a rate of 5.6% compounded semi-annually. The bond matures for C. If the Book Value of the Bond immediately after the 5th coupon is 1100, complete the table with Time, Coupon, Interest, Principal, and Book Value details.

Solution

To solve this problem, we'll analyze the given bond details and complete the table accordingly. Here's the breakdown:

Given Data:

  • Par Value: 1000
  • Yield Rate: 7.6% compounded semi-annually (i.e., 3.8% per period)
  • Coupon Rate: 5.6% compounded semi-annually (i.e., 2.8% per period)
  • Book Value after 5th Coupon: 1100

Key Concepts:

  1. Coupon Payment Calculation:

    • Semi-annual coupon rate = 2.8%×1000=282.8\% \times 1000 = 28.
    • Thus, each coupon payment is 28.
  2. Interest Calculation:

    • The semi-annual yield rate is 3.8%3.8\%.
    • Interest earned for the 5th coupon period is calculated as: Interest=3.8%×1100=41.8\text{Interest} = 3.8\% \times 1100 = 41.8
  3. Principal Adjustment:

    • The principal adjustment is the difference between the book value at the end of the previous period plus the coupon payment and the book value after the current period.

Completing the Table:

Let’s fill in the details using the above calculations.

TimeCouponInterestPrincipalBook Value
5th Coupon2841.830.21100
6th Coupon28TBDTBDTBD
  • For the 5th Coupon:
    • Coupon: 28
    • Interest: 41.8 (calculated above)
    • Principal: Principal=Coupon Payment+InterestChange in Book Value=28+41.81100=30.2\text{Principal} = \text{Coupon Payment} + \text{Interest} - \text{Change in Book Value} = 28 + 41.8 - 1100 = 30.2
    • Book Value: 1100 (given)

Would you like me to proceed with calculating the values for the 6th coupon or clarify any part of the current explanation?

Here are some related questions:

  1. How do bond yields affect the market price of bonds?
  2. What is the difference between the coupon rate and the yield rate?
  3. How do compounding frequencies impact bond valuation?
  4. What happens to bond prices when market interest rates change?
  5. How can one calculate the present value of a bond?

Tip: Understanding how semi-annual compounding works can help you better assess bond returns over different periods.

Ask a new question for Free

By Image

Drop file here or Click Here to upload

Math Problem Analysis

Mathematical Concepts

Bond Valuation
Semi-Annual Yield
Compound Interest
Coupon Payments

Formulas

Coupon Payment = Coupon Rate × Par Value / 2
Yield Rate per Period = Annual Yield Rate / 2
Interest = Yield Rate × Book Value

Theorems

Time Value of Money
Compound Interest
Bond Pricing Adjustments

Suitable Grade Level

Grades 11-12 (or College Level Finance)