Math Problem Statement

Abner​ Corporation's bonds mature in 16 years and pay 12 percent interest annually. If you purchase the bonds for ​$700​, what is your yield to​ maturity?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) of a bond, we can use the following formula for YTM:

YTM=C+FPnF+P2YTM = \dfrac{C + \dfrac{F - P}{n}}{\dfrac{F + P}{2}}

Where:

  • CC = Annual coupon payment = 12%×F12\% \times F (face value)
  • FF = Face value of the bond (typically assumed to be $1000 for U.S. bonds if not specified)
  • PP = Price of the bond (the amount you purchased the bond for, $700)
  • nn = Number of years to maturity (16 years)

First, let's break it down:

  • C=12%×1000=120C = 12\% \times 1000 = 120
  • F=1000F = 1000
  • P=700P = 700
  • n=16n = 16

Now, I'll plug these values into the formula to compute the YTM.The yield to maturity (YTM) on the Abner Corporation bonds is approximately 16.32%.

Would you like more details or have any questions?

Here are 5 related questions to deepen your understanding:

  1. How does the bond's price affect its yield to maturity?
  2. What is the relationship between bond prices and interest rates in the market?
  3. Can you calculate the current yield of this bond, and how does it differ from YTM?
  4. How does YTM change if the bond price increases or decreases?
  5. What are the risks associated with buying bonds at a discount?

Tip: Remember, YTM assumes the bond is held until maturity and that all interest payments are reinvested at the same rate.

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Math Problem Analysis

Mathematical Concepts

Finance
Bond Valuation
Yield to Maturity

Formulas

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

Theorems

Yield to Maturity Formula

Suitable Grade Level

Undergraduate Finance