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

PV = C/(1+i) + C/(1+i)² + ... + C/(1+i)ⁿ + F/(1+i)ⁿ

Part a

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

 PV = F/(1+i)ⁿ

Plugging in the given information,

 Price = $1000/(1+0.1)¹⁵ = $239.39

Thus the price of the fifteen-yr zero coupon bond is $239.39.

Part b

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

Plugging in the given information,

Price = $15/(1+(0.1/2)) + $15/(1+(0.1/2))² +..... + $15/(1+(0.1/2)⁶ + $500/(1+(0.1/2)⁶ = $449.24

Thus the price of the three-yr semiannual 6% coupon bond is $449.24.