The inverse relationship between interest rates and bond prices may seem counter-intuitive, but it is a completely reasonable concept. It's based on the relative value of the bond you hold (which has a fixed interest rate known as the 'coupon rate') compared to the interest rate of the market (which is constantly changing).
Investors are looking to get the most favorable rate they can, and if the interest rate has risen since you purchased your bonds, new bonds will be paying a higher interest rate than the bonds you own. To make your bonds attractive to buyers, you will have to offer them at a discount — in other words, a lower price.
The same principle holds if interest rates fall. A buyer looking to invest in bonds cannot get a better interest rate on new bonds compared to yours. Since your bonds are now more valuable, you can charge a premium if you want to sell them — in other words, at a higher price.
A simple example is the best way to illustrate this concept. If you have purchased $1,000 in a newly issued bond at a fixed 6% coupon rate, you will receive $60 per year in interest on that bond. Let's assume market interest rates go up to 7% shortly after you purchased your bond. Anyone buying a new bond, of equal credit quality, at the same face value of $1,000 will receive $70 per year in interest on the bond. If all other factors were the same, no rational investor would buy your bond when they can receive greater interest on a new 7% bond. You will have to lower the price to make your bond sellable.
Similarly, if the market goes down to 5% at the same time, a new investor would receive $50 per year in interest on that same $1,000 bond. Since the bond you hold returns an extra $10 per year in interest, you can raise the price of the bond to capitalize on this higher value.
While zero-coupon bonds do not provide interest payments (as the interest is paid in a lump sum at maturity), the same principle applies. Instead of comparing earned interest, you are comparing rate of return (the amount you paid for the bond compared to its face value at maturity). For example, if you paid $925 for a zero-coupon bond that paid $1,000 at maturity, your rate of return until maturity is 8.1% ($75 discount divided by the $925 cost). If an investor can get more than 8.1% on new bond issues over the same period because of higher rates, your bond will need to be discounted to make it sellable. Conversely, your bond will command a higher price if an investor cannot match the 8.1% return with new bond issues.
In addition to the interest rate paid, there are many other factors that make bonds more or less attractive to purchase. These factors include credit quality, term, potential for prepayment, and taxability. When assessing the appeal of any bond, you will want to consider all of these factors.
But when comparing bonds of a similar nature and looking only at the effect of interest rate, the inverse relationship between bond prices and interest rates holds true. Bond prices will go up as interest rates fall, and bond prices will go down as interest rates rise.