If you buy both a 30-day Eurodollar CD paying 6.7 percent and a 90-day futures on a 90-day Eurodollar CD with a price implying a yield of 7.2 percent,what is your total annualized return? (Both yields are based on 360-day years. )
A)7.25 percent
B)7.07 percent
C)10.15 percent
D)7.75 percent
E)6.95 percent

Question

Quizplus · Accepted Answer

To calculate the total annualized return when you buy both a 30-day Eurodollar CD paying 6.7 percent and a 90-day futures on a 90-day Eurodollar CD with a price implying a yield of 7.2 percent, we need to consider each investment separately and then combine them to find the total return.
First, let's calculate the return on the 30-day Eurodollar CD:
The annualized return on the 30-day CD can be calculated using the formula for simple interest:
$$ \text{Annualized Return} = \left( \frac{\text{Interest Rate}}{\text{Days in Period}} \right) \times \text{Days in Year} $$
For the 30-day CD at 6.7%:
$$ \text{Annualized Return}_{30-day} = \left( \frac{6.7\%}{30} \right) \times 360 = 80.4\% $$
This is not realistic as it does not account for the fact that the CD is only held for 30 days out of the year. We need to adjust this to reflect the actual period of the investment:
$$ \text{Actual Return}_{30-day} = \left( \frac{6.7\%}{360} \right) \times 30 = 0.5583\% $$
Now, let's calculate the return on the 90-day futures contract:
The annualized return on the 90-day futures contract can be calculated in a similar manner:
For the 90-day futures at 7.2%:
$$ \text{Annualized Return}_{90-day} = \left( \frac{7.2\%}{90} \right) \times 360 = 28.8\% $$
Again, we need to adjust this to reflect the actual period of the investment:
$$ \text{Actual Return}_{90-day} = \left( \frac{7.2\%}{360} \right) \times 90 = 1.8\% $$
Now, we need to combine the returns. Since the 30-day CD matures first, you can reinvest the return from the CD into the futures contract. However, the question does not specify what happens to the proceeds from the CD after 30 days, so we will simply add the returns together for the total return over the 90-day period:
$$ \text{Total Return} = \text{Actual Return}_{30-day} + \text{Actual Return}_{90-day} $$
$$ \text{Total Return} = 0.5583\% + 1.8\% = 2.3583\% $$
This is the total return over the 90-day period. To annualize this return, we need to account for the fact that there are four 90-day periods in a 360-day year:
$$ \text{Annualized Total Return} = \text{Total Return} \times 4 $$
$$ \text{Annualized Total Return} = 2.3583\% \times 4 = 9.4332\% $$
This result does not match any of the options provided in the question. It's possible that there may be a mistake in the calculation or in the interpretation of the question. However, based on the information given and the standard method of calculating annualized returns, the annualized total return would be approximately 9.43%, which is closest to option C) 10.15 percent. Please note that this calculation assumes that the returns are not compounded, as compounding would slightly alter the result.

If You Buy Both a 30-Day Eurodollar CD Paying 6