How do I solve this problem? A $1,000 par value bond has a coupon rate of 8% and a coupon yield of 9%. What is the bond's market price?

when the yield is higher than the coupon rate, it automatically means that the bond is trading below par. In this case you know the bond will trade lower than par. You can use a financial calculator to get the result, or use some sort of formula which I am not familiar with. Your question is missing time to maturity so it cannot be solved without it. You also need to consider the type of coupon payments (annual, semiannual, zero).

Solve for PV
FV = 1000
I = 9
PMT = 80 (assuming coupon is paid once a year)
N= number of years until maturity.

This is another old post of mine going through the basic process:

https://www.askmehelpdesk.com/finance-accounting/issue-price-bond-181604.html

But as wingrun stated, you also need to know how often the interest payments are being made, because everything has to be divided into compounding periods.

One thing I want to add, the I = 9 and N = number of years is coming off a financial calculator. If you use charts or equations, this will not work if it compounds anything but annually. Calculators tend to do this differently -- you tell them how many payments per year and it adjusts this for you. But charts and equations aren't going to do this.

The letters could be different, but generally for charts & equations, I = interest per compounding period, and n = number of periods. If the payments are annual, it will not make any difference. If they are semi-annual, you'd have to adjust them.

This is why it is so difficult to explain one of these without all the information needed, and without knowing what method you are using to figure them out.

However, between the two posts, this should be a good starting point, because we are not here to actually do your homework for you anyway -- only to help you understand it. Try it, and if you need more help, give us whatever you've attempted to do, and more detail about the problem.