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Pricing a three-year annual-coupon bond payment by payment

A face value of 100, annual coupon of 5 and annual yield of 6% give a three-year coupon-date price of 97.327. Each payment is discounted separately.

Identify the payment stream

The first two years each pay a coupon of 5. Year three pays the final coupon of 5 and principal of 100, so that final cash flow is 105. Returning principal is not an extra coupon and must not be omitted.

Discount each payment at 6%

The payments arrive one, two and three years from the pricing date. Use powers of 1.06 that match those times. Add the discounted amounts, keeping rounding until the final presentation.

P=51.06+51.062+1051.063P=\frac{5}{1.06}+\frac{5}{1.06^2}+\frac{105}{1.06^3}

The example prices at a coupon date with annual compounding.

Present values of the promised payments
YearCash flowPresent value
154.717
254.45
310588.16

Check the direction and scope

The coupon rate is 5%, below the 6% yield, so a price below face value is consistent with the fixed-cash-flow model. The payment stream is unchanged if the required yield changes; only the discounting changes. An accrued-interest adjustment or an irregular first period would require additional timing information.

Further references