In order to calculate effective duration, we first need to know the bond price if interest rates rise or fall by 50 basis points.

For the Yorkville bond:

N = 24; PMT = (0.059 coupon × $1,000 par value / 2 payments per year =) 29.50; FV = 1,000

If rates rise by 50 basis points, I = ((5.9% + 0.50 =) 6.4% / 2 payments per year =) 3.2%; PV = -958.56.
Since the bond has a par value of $1,000, the estimated price will be (958.56 / 1,000 × 100 =) 95.86.

If rates fall by 50 basis points, I = ((5.9% − 0.50 =) 5.4% / 2 payments per year = ) 2.7%; PV = -1043.74.
Since the bond has a par value of $1,000, the estimated price will be (1043.74 / 1,000 × 100 =) 104.37.

Now that we have the prices, we can use the formula for effective duration (ED):

ED = (104.37 – 95.86) / (2 × 100 × 0.005)
ED = 8.51 / 1
ED = 8.51

For the Mountain States bond:

N = 24, PMT = (0.052 coupon × $1,000 par value / 2 payments per year =) 26.00, FV = 1,000

If rates rise by 50 basis points, I = ((5.2% + 0.50 =) 5.7% / 2 payments per year =) 2.85%; PV = -956.97.
Since the bond has a par value of $1,000, the estimated price will be (956.97 / 1,000 × 100 =) 95.70.

If rates fall by 50 basis points, I = ((5.2% − 0.50 =) 4.7% / 2 payments per year =) 2.35%; PV = -1045.46.
Since the bond has a par value of $1,000, the estimated price will be (1045.46 / 1,000 × 100 =) 104.55
However, since the bond is callable at 102, the price will be 102, not 104.55.

ED = (102 – 95.70) / (2 × 100 × 0.005)
ED = 6.30 / 1
ED = 6.30

The ED of the Yorkville bond is (8.51 – 6.30 =) 2.21 higher than the ED of the Mountain States bond.