Answer:
d. 6.8%
Explanation:
The one year bond has a coupon rate of 5% per year.
- For 6 months in order to have a payment of 1000 we need a face value of 1000/1.025 = 975.61.
- Coupon payments of 975.61 x .025 = 24.39 at time 0.5 and time 1,
- Payment of the par amount of 975.61 at time 1.
Total cash flow = 1000.
We compute the price of these bonds by discounting their cash flows at their yields:
1-year bond: Price = 24.39 x 1.035^-1 + 1000 x 1.035^-2 = 957.08
6-month bond: Price = 975.61 x 1.03^-1 = 947.19
Total Price = 957.08 + 947.19
Total Price = 1904.27
So, the required yield for the combined cash flows can be found by solving:
1904.27 = 1000v + 1000v^2
EffectIve rate per 6 months = 3.3332%
Annual effective yield basis = 1.03332^2 - 1
Annual effective yield basis = 1.0677502224 - 1
Annual effective yield basis = 0.0677502224
Annual effective yield basis = 6.8%
