Tech Crunch, a local technology store, wants to evaluate the average price of their headphones sold in the past week, so the manager reviews the sales data. They determine the store sold 8 sets of headphones at prices of $44.57, $76.43, $56.25, $123.52, $235.22, $189.78, $190.34, $267.45. The manager combines the prices to determine a sum of $1,183.56. To determine the average price, the manager divides the sum by the total amount of headphones sold. The average price of the last week of headphone sales at Tech Crunch was $147.94.
Example of calculating the average price in a yield to maturity (YTM) formulaAn investor purchases a bond with a coupon rate of 6% and five years to maturity for $1,200. With a face value of the bond of $1,000, the investor calculates the annual 6% coupon payments at $60. The investor enters the information into the YTM formula to determine the following:Yield to maturity = (Cash flow + ((Face value - Market value) / Years to maturity)) / ((Face value + Market value) / 2)Yield to maturity = $60 + (($1,000 - $1,200) / 5) / (($1,000 + $1,200) / 2)Yield to maturity = $20 / $1,100Yield to maturity = 1.82%The investor uses this to determine that even though they receive a $60 annual coupon, the real or average return is $20 per year. This decrease in return is because the investor bought the bond above par.