Final answer:
To approximate the current yield to maturity of a bond, you must consider the annual coupon payments, the purchase price, the face value, and the time until maturity. The exact calculation is complex and requires a financial calculator or formula, but a simplified formula can provide an estimate of the yield to maturity.
Step-by-step explanation:
To calculate the current yield to maturity (YTM) of the XYZ April 2041 bond with a 5.5% coupon rate and a price of 95.625, we will use the bond's coupon payments, face value, and current price. The bond pays annual interest of 5.5% of its $1,000 face value, which equals $55 per year. The bond is currently priced at $956.25 (since 95.625% of $1,000 is $956.25). The yield to maturity will factor in the annual coupon payments, the difference between the purchase price and the face value, and the time remaining until maturity.
First, calculate the annual coupon payment:
$1,000 * 5.5% = $55. Then, find the difference between the face value and the price: $1,000 - $956.25 = $43.75. Lastly, distribute this difference over the years remaining until the bond matures.
Assuming the bond has 18 years until maturity, the approximate YTM will consist of the annual coupon payment and the average annual gain from the difference between the current price and the face value.
The approximate YTM calculation is more complex and usually requires a financial calculator or a specific formula, as it involves solving for the discount rate that equates the present value of all future cash flows (coupon payments and face value) to the bond's current price. However, a simplified approximation would be:
(Annual Coupon Payment + (Face value - Current price) / Years to Maturity) / ((Face value + Current price) / 2).