Math Problem Statement

​(Related to Checkpoint​ 9.2) ​(Yield to​ maturity) Abner​ Corporation's bonds mature in 17 years and pay 13 percent interest annually. If you purchase the bonds for ​$1 comma 225​, what is your yield to​ maturity? Question content area bottom Part 1 Your yield to maturity on the Abner bonds is

enter your response here​%. ​(Round to two decimal​ places.)

Solution

To calculate the yield to maturity (YTM) for Abner Corporation's bonds, we can use the following formula for YTM approximation:

YTMC+FPnF+P2YTM \approx \frac{{C + \frac{{F - P}}{{n}}}}{{\frac{{F + P}}{2}}}

where:

  • CC = Annual coupon payment
  • FF = Face value of the bond (usually assumed to be $1,000 if not stated)
  • PP = Price of the bond (purchase price)
  • nn = Years to maturity

Given dataTo calculate the yield to maturity (YTM) for Abner Corporation's bonds, we can use the following formula for YTM approximation:

YTMC+FPnF+P2YTM \approx \frac{{C + \frac{{F - P}}{{n}}}}{{\frac{{F + P}}{2}}}

where:

  • CC = Annual coupon payment
  • FF = Face value of the bond (usually assumed to be $1,000 if not stated)
  • PP = Price of the bond (purchase price)
  • nn = Years to maturity

Given

  • Coupon rate = 13% (so, C=0.13×1,000=130C = 0.13 \times 1,000 = 130 annually)
  • Price P=1,225P = 1,225
  • Years to maturity n=17n = 17
  • Face value F=1,000F = 1,000 (assuming this is standard if not stated otherwise)

Let's plug these values into the approximation formula to get an initial estimate. However, for precise YTM calculation, using a financial calculator or iterative method like Excel's RATE function is typical. I'll calculate the approximate YTM first.The approximate yield to maturity (YTM) for Abner Corporation's bonds is 10.50% (rounded to two decimal places).

Would you like a detailed explanation of the steps, or do you have any additional questions?

Here are some related questions that might deepen your understanding:

  1. How does the bond price affect the yield to maturity?
  2. What is the impact of time to maturity on the YTM calculation?
  3. How does a bond's coupon rate compare to its YTM?
  4. What are other methods to calculate YTM more precisely?
  5. How does YTM differ from the bond’s current yield?

Tip: YTM calculations typically assume that all coupon payments are reinvested at the same rate as the YTM, which may not always be practical in real-world scenarios.

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Math Problem Analysis

Mathematical Concepts

Finance
Yield to Maturity (YTM)
Bond Pricing

Formulas

YTM ≈ (C + (F - P) / n) / ((F + P) / 2)

Theorems

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Suitable Grade Level

College or Advanced High School (Grades 11-12)