Suppose a seven-year, $ 1 comma 000 bond with a 7.8 % coupon rate and semiannual coupons is trading with a yield to maturity of 6.50 %. If the yield to maturity of the bond rises to 7.20 % (APR with semiannual compounding), what price will the bond trade for?

The price of the bond is 1,072.19

Explanation:

The price at which the bond trades for can be computed using the pv formula in excel which tries to discount to present value all the cash inflows receivable from the bond into today's present worth.

=-pv (rate, nper, pmt, fv)

rate is the yield to maturity of 6.50% divided by 2 since the bond pays interest semi-annually i. e 3.25%

nper is the number of coupon payments the bond would pay which is 7 years multiplied by 2 i. e 14

pmt is the semi-annual interest of the bond which is $1000*7.8%/2=$39

the fv is the face value of the bond of $1000

=-pv (6.5%/2,14,39,1000) = $1,072.19