A bond with a $1,000 face value and an 8 percent annual coupon pays interest semiannually. The bond will mature in 15 years. The nominal yield to maturity is 11 percent. What is the price of the bond today?

The price of the bond today is $784.27

Explanation:

Face value (FV) : $1000

Coupon rate: 8% - > counpon received annually (PMT) is $80 ( = $1000 * 8%)

Tenor: 15 years

YTM: 11%

Present value = Future Value / (1 + YTM) ^tenor

We can use excel to calculate Present Value of annual payment = PV (Rate, tenor,-PMT) = PV (11%,15,-80) = $575.27

The price of bond today = present value of face value + present value of coupon received annually

= 1000 / (1+11%) ^15 + 80 / (1+11%) ^15 + 80 / (1+11%) ^14 + ... + 80 / (1+11%) ^1

= 1000 / (1+11%) ^15 + $575.27

= $784.27