I can buy a $1,000 bond for $950. I get $50 a year and it matures in 20 years. I want to know what interest rate I am earning
To calculate the interest rate you are earning on the bond, we can use the formula for yield to maturity (YTM). Yield to maturity is the total return anticipated on a bond if it is held until it matures.
The formula for YTM is as follows:
YTM = [(Annual interest payment + (Face value - Purchase price) / Number of years held)] / [(Face value + Purchase price) / 2]
Let's calculate the YTM for your bond:
Annual interest payment = $50
Face value = $1,000
Purchase price = $950
Number of years held = 20
Plugging these values into the formula:
YTM = [($50 + ($1,000 - $950) / 20)] / [($1,000 + $950) / 2]
First, we can calculate the part in the numerator:
YTM = [($50 + $50) / 20] / [($1,000 + $950) / 2]
YTM = [$100 / 20] / [$1,950 / 2]
YTM = $5 / $975
Now, divide the numerator by the denominator:
YTM = 0.0051
Finally, convert this decimal into a percentage by multiplying by 100:
YTM = 0.0051 * 100
YTM = 0.51%
Therefore, the interest rate you are earning on the bond is approximately 0.51%.