I've been reading that there is an inverse relationship between fixed-rate bonds and interest rate. The explanation behind the reasoning is that as interest rates move, the bond has to compete with new bonds so the price of the bond syncs up the bond's yield with the current interest rate. I found this doc from sec.gov that has a good explanation: https://www.sec.gov/files/ib_interestraterisk.pdf
In Example 2: If Market Interest Rates Increase by One Percent, the face value of the bond is $1000 but with an increase interest rate of 1% a year later (to 4%), the bond is only worth $925. The concept makes sense since the yield to maturity of the bond then matches the new interest rate of 4%.
Why would anyone sell the bond at $925? Aren't they losing both $75 that they paid originally for the bond AND the interest payments over the next couple of years on the bond? Since people do sell at a lower price, what am I missing here?