YTM can be determined using the price formula of a bond.

Part a

The present value (price) formula for a zero coupon bond is:

PV = F/(1+i)ⁿ

Plugging in the given information,

$300 = $1000/(1+i)¹⁵

(1+i)¹⁵ = 3.33

1+i = 1.08357

i = YTM = 0.08357 = 8.36%

Thus the YTM of the fifteen-yr zero coupon bond is 8.36%.

Part b

Semiannual coupon = 6%*$500/2 = $15

Plugging in the given information,

Price = $15/(1+(i/2)) + $15/(1+(i/2))² +..... + $15/(1+(i/2)⁶ + $500/(1+(i/2)⁶ = $400

On trial and error using Excel, YTM has been determined to be 7.23%.

Thus the YTM of the three-yr semiannually 6% coupon bond is 14.45%.