What causes the inverse relationship between interest rates and bond prices?

The fact that the bond price is lower is what causes a higher yield in the first place. using the approximate yield to maturity formula (see the fixed income chapter in your text), take a look at the following 3 scenarios that should help explain the relationship:assume a bond that pays 5% per year in interest, matures in 4 years and trades at 100.according to the approximate yield to maturity formula, the yield of this bond would be:= (interest income + annual price change)/ [(100 + bond price)/2]= ($5 + $0) / [(100 + 100)/2] = 5%what happens if interest rates rise in the market? the existing bond wont be as valuable because new issuers will issue bonds with a coupon rate that provides more interest income in order to keep pace with the higher market interest rate. so assume the price of the bond above was now at 96 instead of 100.the approximate yield to maturity would be:= ($5 + $1) / [(100 + 96)/2]= 6.12%why is the yield higher if the bond price is lower? yield consists not only of the interest income earned each year, but also includes the theoretical gain or loss per year based on the difference between the purchase price and maturity price. the bond is now at 96, so if an investor were to buy that bond today, he or she would enjoy not only $5 in interest income each year, but also would gain $1 per year in value (since he or she paid 96 but will get back 100 in 4 years).what if, rather than rising, market interest rates had fallen. this would lead to a higher bond price since the bond in existence would pay more interest than what new issuers are offering. the existing bond would be more attractive to buyers. lets say the bond price increased to 104. what would the approximate yield to maturity be?= ($5 - $1) / [(100 + 104)/2]= 3.92%since the investor today would pay 104 for something that ill only pay back 100 in 4 years, the investor is theoretically losing $1 per year. so even though the investor gains $5 from interest income, the investor also loses $1 per year.the reason why yield moves in the opposite direction to price, as mentioned earlier, is that yield includes both interest income and gain or loss.