1 · Price and yield are one number seen twice
The payments are frozen, so the price is the only thing left that can move. Drag the yield the market demands and watch what the paper is worth.
price = Σ coupon/(1+y)^t + face/(1+y)^n · duration = the slope of this curve, right where you are standing
4.00%
10 yr
4.00%
price per $100
100.00
duration
8.1
if yields +1%
−7.7%
Duration is the gradient in one number: roughly the percent you lose when yields rise a single point. Long bonds are not safer, they are more leveraged — a longer chain of future cash that has to be repriced when the discount changes.