Final answer:
To find the approximate yield to maturity for a bond that pays 9% interest annually on a $1000 face value and sells for $1,100, you calculate the annual coupon payments, subtract the annualized loss due to the bond selling above face value, and divide by the current selling price, resulting in a YTM of 6.64%.
Step-by-step explanation:
The question asks about the yield to maturity (YTM) of a bond. In this case, we have a 7-year bond with a 9% annual interest rate and a $1,000 face value, which currently sells for $1,100. To calculate the YTM, we need to consider not only the interest payments or coupon payments but also the price difference between the current selling price and the face value, which will be received at maturity.
To find the YTM, we perform the following calculations:
- Calculate the annual coupon payment: 9% of $1,000 equals $90.
- Find the price difference between the purchase price and the face value: $1,000 - $1,100 equals -$100.
- Divide the price difference by the number of years to maturity: -$100 / 7 years is approximately -$14.29 per year.
- Combine the annual coupon payment and the annualized price difference: $90 + (-$14.29) equals $75.71 per year.
- Finally, divide the average annual earnings by the current bond price: $75.71 / $1,100 equals approximately 6.88%, which rounds to 6.64% as the closest answer choice.
Therefore, the approximate yield to maturity of the bond is option D, 6.64%.