A 10 year bond pays 11% interest on a $1000 face value annually. If it currently sells for $1,195, What is its approximate yield to maturity?
a)9.33%
b)7.94%
c)12.66%
d)8.10%
8.10
To find the approximate yield to maturity of a bond, you can use a financial calculator or a spreadsheet program. However, I will explain how to calculate it using a simplified method.
The yield to maturity (YTM) is the total return anticipated on a bond if it is held until it matures. It is expressed as an annual percentage rate. In this case, we know the bond has a face value of $1000, pays 11% interest annually and currently sells for $1195.
To calculate the approximate yield to maturity, you can follow these steps:
Step 1: Calculate the total interest payment
Total interest payment = face value x interest rate
Total interest payment = $1000 x 11% = $110
Step 2: Calculate the gain or loss
Gain or loss = current price - face value
Gain or loss = $1195 - $1000 = $195
Step 3: Calculate the average annual gain or loss
Average annual gain or loss = (gain or loss) / years until maturity
Since the bond is a 10-year bond, the years until maturity is 10.
Average annual gain or loss = $195 / 10 = $19.5
Step 4: Calculate the yield to maturity
YTM = (Total interest payment + Average annual gain or loss) / current price
YTM = ($110 + $19.5) / $1195
YTM ≈ 0.1054 ≈ 10.54%
Therefore, the approximate yield to maturity is approximately 10.54%.
None of the options provided matches this result, so it seems there might be an error in the given options. Please double-check the answer choices or refer to a financial calculator or spreadsheet program for a precise calculation.
To calculate the approximate yield to maturity (YTM) of the bond, we can use the formula:
YTM = (Annual Interest Payment + (Face Value - Current Price) / Number of Years) / ((Face Value + Current Price) / 2)
Plugging in the given values:
Annual Interest Payment = $1000 * 11% = $110
Face Value = $1000
Current Price = $1195
Number of Years = 10
YTM = ($110 + ($1000 - $1195) / 10) / (($1000 + $1195) / 2)
Simplifying the equation:
YTM = ($110 + (-$195) / 10) / (($1000 + $1195) / 2)
YTM = ($110 - $19.50) / (($2000) / 2)
YTM = $90.50 / $1000
YTM = 0.0905
Converting the decimal to a percentage:
YTM = 0.0905 * 100%
YTM ≈ 9.05%
Therefore, the approximate yield to maturity of the bond is 9.05%, which is closest to 9.33%, so the correct answer is option a) 9.33%.