What would you pay for a bond that pays an annual coupon of $45, has a
face value of $1,000, matures in 11 years, and has a yield to maturity
of 10%?

$642.77

I agree with the previous answer to a degree.  The net present value
of that investment is $642.77.  This can be calculated using the NPV
function within Excel.

However, the amount I am willing to pay for that investment is
dependent upon the market interest yields for similar instruments of
similar maturities.  If the current market demands a 12% yield yet
this instrument returns only 10%, I will discount my purchase
price...Is this where you were going?