The general approach to bond valuation is to utilize a series of spot rates to reflect the timing of future cash flows.

The bond pays a 5% annual coupon on a $1,000 face value, so each coupon payment is $50. The final payment at year 3 includes the coupon plus the face value = $1,050.

Using the appropriate spot rates for each cash flow:

• Year 1 cash flow of $50 discounted at 1-year spot rate of 3%
• Year 2 cash flow of $50 discounted at 2-year spot rate of 4%
• Year 3 cash flow of $1,050 discounted at 3-year spot rate of 5%

$(50/1.03) + (50/1.04^2) + (1,050/1.05^3) = 1,001.80$

The key concept here is that each cash flow must be discounted using the spot rate corresponding to the time period when that cash flow is received, not a single yield-to-maturity rate. This is the no-arbitrage approach to bond pricing using the spot rate curve.