Why would Investors care if their Bonds' Market interet rate INCREASES...aren't they getting paid the same?

Yes, the bond holder still receives their 10% and the face value but they would not be able to sell their 10% bonds when competing against 15% bonds of similar risk hence they would have to discount the price of their bonds such that the purchaser effectively gets a 15% yield on those 10% bonds. That means, the value of the holdings has decreased. If they decide to hold the stock instead of selling, they are simply forgoing the opportunity of other investment opportunities that returned 15% but seeing as they would have to first sell their 10% bonds at a discount, there would be little reason to change investments other than the receive more of the return earlier. Of course, nothing is stopping the investor from investing more into the higher rates which is why budgeting your paycheck to include a regular amount for investing is important.

Yes, he would still be paid the $1000 at maturity and he will still collect the 10%. The problem arises because the market price has fallen for some specific reason that is most likely not all that advantageous to the purchaser of the bond. The two most likely reasons are 1. the bond is very likely to go into default which would mean kissing most if not all of the $1000 goodbye 2. inflation has increased dramatically and the 10% interest is now a loosing proposition. Not only that buy when the bond is redeemed the original $1000 might then be worth only $300.

Not everyone invests in bonds to collect interest. Many investors want the VALUE of their bonds to increase, meaning they want interest rates to drop. When interest rates increase, the value of bonds decreases because bond holders are stuck holding an investment that pays less than market rates.

The bondholder would still get the same 10 percent interest and $1000 at maturity. But holders of newer bonds are getting a higher interest rate plus the $1000 at maturity. The market value of the original bonds will drop also if investors want to sell before maturity. So holders of the new bonds will get a higher return while holders of the older bonds are still getting paid the same.