Suppose a ten-year, $1000 bond has an 6% coupon rate and semiannual coupons. If the bond’s yield to maturity is 8% (an APR with semiannual compounding), what is the bond’s price?

The price of the bond today is $ 864.10  

Explanation:

In calculating the bond's price today,I need to discount all the future cash flows of the bond over the ten years to present value in order to arrive at the price of the bond.

It might be interesting to note that the future cash flows in this sense refer to the semi-annual payment of the bond coupon interest and finally the repayment of the principal at year 10.

Since, coupon interest is expected to be paid every six  months,the number of coupon payments is 20( 10 years paid twice every year).

The applicable discount factor is 1/(1+r)^N where r is the yield to maturity divided by 2 as 8% is annual interest rate and N is the relevant year that the cash flow belongs to.

The present valuing is done in the attached spreadsheet.

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