Inverse Relationship between bond prices and Interest Rates

We always hear experts saying that when interest rate increases, bond prices fall. More directly, there is an inverse relationship between bond prices and interest rates. Why is that so?

Let us consider using zero coupon bonds. A zero coupon bond, as defined by Investopedia, is a debt security that doesn't pay interest (a coupon) but is traded at a deep discount, rendering profit at maturity when the bond is redeemed for its full face value.

So now assuming a customer buys a zero coupon bond for $1000. At maturity 1 year later, he gets back $1050. From here, we can see that the interest rate paid by the bank to the customer is (1050-1000)/1000 x 100% = 5%.

If the interest rate provided else where apart from buying these bonds are lower, consumers will want to stick with the bonds as they pay higher interest.

If interest rate elsewhere increases to more than 5%, then consumers will want to sell their bonds at maturity, get the cash and place it somewhere else where it can earn higher interest i.e. demand for bond reduces. When the bonds are sold, supply of bonds increases and thus the price of bonds will drop using the basic demand and supply model.

Conversely, when the interest rate offered is lower than the interest rate provided by buying bonds, or that interest rate has dropped, then consumers will demand and buy bonds as it offers a higher interest. When purchase of bond occurs, the increased demand will push the price of the bonds up.

From here, we can evidently see that a inverse relationship exists between interest rate and bond prices.