Amy purchased a five-year $5,250 bond below par value for $4,675 with a coupon of 3.5%. What was her yield?
the answer is 3.9%
To calculate the yield, also known as the yield to maturity (YTM), we need to take into account the price paid for the bond, the coupon rate, and the time period until the bond matures.
The formula to calculate yield is as follows:
Yield = (Annual Interest + (Face Value - Purchase Price) / Years to Maturity) / Purchase Price
Let's break down the information given in the question:
- The face value of the bond is $5,250.
- Amy purchased the bond below par value for $4,675.
- The coupon rate is 3.5% (which means Amy will receive 3.5% of the face value as interest each year).
- The bond has a five-year maturity period.
Using the formula above, we can calculate the yield:
Annual Interest = Face Value * Coupon Rate
Annual Interest = $5,250 * 0.035
Annual Interest = $183.75
Yield = (Annual Interest + (Face Value - Purchase Price) / Years to Maturity) / Purchase Price
Yield = ($183.75 + ($5,250 - $4,675) / 5) / $4,675
Yield = ($183.75 + $475) / $4,675
Yield = $658.75 / $4,675
Yield ≈ 0.141 or 14.1%
Therefore, Amy's yield on the bond is approximately 14.1%.