A University of Colorado revenue bond pays an 8% level-coupon, matures in three years, and offers an effective annual yield (i.e., true yield)of 6%. The bond has a principal value of $1,000
And pays interest semiannually. What is the value of this bond, to the nearest dollar?

Question

Quizplus · Accepted Answer

Using the bond pricing formula with semi-annual payments:

P = (C/r) (1 - 1/(1+r)^n) + 1000/(1+r)^n

where P is the price of the bond, C is the semi-annual coupon payment (which is $40: 0.08/2 * 1000), r is the semi-annual yield (which is 0.06/2), and n is the number of semi-annual periods (which is 6).

Plugging in these values, we get:

P = (40/0.03) (1 - 1/(1+0.03)^6) + 1000/(1+0.03)^6
P = $1,054.13

Rounding to the nearest dollar, we get the answer of $1,054, which is choice B. Using the effective annual yield formula:
(1 + (0.06/2))^2 - 1 = 0.059 = 5.9% semiannual yield
Using the present value of a bond formula: 
P = (C/r) x [1 - (1 + r)^-n] + FV/(1+r)^n
where P is the price, C is the coupon payment, r is the semiannual yield, n is the number of semiannual periods, and FV is the face value of the bond. 
P = (40/0.059) x [1 - (1+0.059)^-6] + 1000/(1+0.059)^6
P = $1,053.53 ≈ $1,054. Therefore, the best choice is B.

A University of Colorado Revenue Bond Pays an 8% Level-Coupon