A bond's price is the present value of all its future cash flows, which consist of periodic coupon payments and the return of face value at maturity. The pricing formula is: Price = C × [1 - (1+r)^-n] / r + FV / (1+r)ⁿ, where C is the coupon payment per period, r is the yield per period, n is the total number of periods, and FV is the face value. This discounted cash flow approach is the foundation of bond valuation.

When market yields rise above a bond's coupon rate, the bond price falls below par (trading at a discount) because investors demand compensation for the lower-than-market coupon. Conversely, when yields fall below the coupon rate, the bond trades at a premium because its coupon payments are more attractive than what the market currently offers. At par, the coupon rate equals the yield.

Payment frequency matters because it affects compounding. A semi-annual bond paying 5% delivers two payments of 2.5% each, and the yield is also divided by two for discounting. More frequent payments slightly increase the present value of coupon cash flows, resulting in a marginally higher price compared to an annual-pay bond with the same coupon and yield.