Question

1. If you were to purchase a fifteen year T-Note with a 2.8% YTM, what would its price (assuming a semiannual PMT) be it its coupon rate is 2.5%?

Also, briefly explain the relationship between the YTM, the coupon rate, and the price…starting the math in solving for PV? Why is the price higher/lower than par?

Answer 1

Calculation of Price:

FV = 1000
Nper = 15 * 2 = 30
PMT = 1000 * 2.5% / 2 =12.50
Rate = 2.8% / 2 = 1.4%

Price can be calculated by using the following excel formula:
=PV(rate,nper,pmt,fv)
=PV(1.4%,30,-12.50,-1000)
= $963.46

Price = $963.46

YTM and Price are inversely related. If the YTM increases, then the price will decreases. If the YTM decreases, the price will increases.

If the YTM is greater than coupon rate, then the price will lower than the par value. If the YTM is less than the coupon rate, then the price will higher than par value.