Determine the cash price of a 6% Treasury bond that matures in 14 months using the zero rates below. The Treasury bond has semiannual coupon payments.
First, I calculated the coupon payments. There are two full coupon payments at months 6 and 12. At month 14 I tired to add the accrued interest. This part is what I'm struggling with the most. How do I account for the cash flow for the last 2 months.
For months 6 and 12 = .06/2 *100 = 3
For month 14 = 2/6 * 3 = 1
Since the zero rates are semiannual compounding I need to convert them to continuous compounding.
2*ln(1+.06/2) = 0.0591
2*ln(1+.12/2) = 0.1165
2*ln(1+.14/2) = 0.1353
The cash price is the present value of the clash flows. And since it is continous compounding is use the following equation to determine the price of the bond.
3e(-.0591*.5)+3e(-.1165*1)+101e(-.1353*1.1667)=91.8341
Hint: If the bond matures in 14 months, I'd think the coupons are due in 2, 8 and 14 months, not in 6 and 12 (and partially 14) months. This is because I'm fairly sure that Treasury bonds are issued with maturities of whole years (20-30 years actually; although whole half years would give the same). This (also) implies that the Treasury bond in the question was issued earlier, not "now".
Also see: https://en.wikipedia.org/wiki/United_States_Treasury_security#Treasury_bond