Find the present value of a 2-year Treasury bond that pays a semi-annual coupon, has a coupon rate of 6%, a yield to maturity of 5%, a par value of $1,000 when the yield to maturity is 5%.

Question

Quizplus · Accepted Answer

First, we need to calculate the semi-annual coupon payment, which is ($1,000 x 6%)/2 = $30. 
Next, we can use the present value formula to calculate the current price of the bond: 
PV = (C/2)/(1 + y/2) + (C/2)/(1 + y/2)^2 + … + (C/2 + FV)/(1 + y/2)^4 
where C is the semi-annual coupon payment, y is the yield to maturity, and FV is the par value. 
Plugging in the numbers: 
PV = ($30/1.025) + ($30/1.025)^2 + ($30/1.025)^3 + ($30/1.025)^4 + ($1,000/1.025)^4 
PV = $28.89 + $28.00 + $27.12 + $26.24 + $889.57 
PV = $1,018.81.

Find the Present Value of a 2-Year Treasury Bond That