What is the logic for the inverse relationship between interest rates and bond prices?

When interest rates are higher than when the bond was first issued, the price of thebond drops below par. when interest rates are lower than when the bond was firstissued, the price of the bond rises above par.example: an issuer wants to raise money by issuing bonds. the current marketinterest rate is around 5%, so the issuer knows that a 5% coupon rate is required toattract interest in the bond. lets say the issuer sells the bonds at a price of 100 (par)with a 5% coupon rate. i decide to buy the bond and pay $100.a year later, market interest rates jump to 10%. a new issuer decides to raise moneyby issuing a bond. the issuer knows that since market interest rates are around 10%,the issuer will have to offer a bond that pays investors at least 10%, since thats whatpeople expect as a return on their investment. so the issuer sells a bond with acoupon rate of (10% at a price of 100 (par).you now decide to jump in the market and buy a bond. you have two choices: (1) buyan existing bond from someone like me; or (2) buy a bond from a new issuer.if you buy a bond from the new issuer, it will cost you $100 to buy a bond that pays you10% interest income per year. would you be willing to hand over the same $100 to buymy bond that pays only 5% interest income per year? in order for me to sell my bondto you, i will definitely have to drop my price. in fact, i will drop the price of my bonduntil the yield is close to 10%.from this you can see that because interest rates went up, the price of existing bondshad to go down. since the current market interest rate of 10% exceeds the rate at thetime of the bond issue i bought, the price of my bond will be well below par.so how does the yield on my bond go up if i drop my price?the best way to answer that is to use the approximate yield to maturity.assume a 5% coupon bond that matures in 5 years and market interest rates arecurrently around 5%. the price of the bond is 100.aym = annual income + annual price change / average priceannual income: 5% x $100 = $5 per yearannual price change: there is no change since the bond price is 100 and at maturity iwill receive 100.aym = $5 + $0 / ([$100 + $100]/2)aym = 5%(from this you can see that when the coupon rate and market interest rate are thesame, the price of the bond is 100 and the yield is the same as the coupon rate.)now what happens if market interest rates are at 10%? ill probably drop the price ofmy bond to somewhere around 80:aym = annual income + annual price change / average priceannual income: its still $5 (5% x $100)annual price change: if you buy my bond at 81 and it matures at 100 in 5 years, youwill gain $20 in 5 years or $4.00 per year.aym = $5 + $4.00 / ([$80 + $100]/2)aym = 10%so by dropping my price to $80, the yield on the bond rises to 10% and is now anattractive option to you if you are interested in buying a bond. you could buy the bondfrom the new issuer and pay $100 and receive a yield of 10%, or you could buy mybond and pay $80 and receive a yield of 10%. the only differences are the issuers inquestion (you might like one issuer over the other), and the fact that some of the yieldyou receive from my bond is a result of capital gains rather than just interest income.an important consideration is that a portion of the gain you receive from buying mybond will be taxed as a capital gain which calls for a lower taxation rate than anyinterest income received, but you wont realize that gain immediately in the form of anannual cash flow.