Sure, let's break down this problem step-by-step to determine the yield of the investment.
### Step 1: Identify the important information
- Amount invested: \[tex]$11,000
- Interest rate: 2.3% per annum (or 0.023 when expressed as a decimal)
- Days invested: 91 days
- Broker's commission: \$[/tex]20
- Days in a year for treasury bills: 360 days
### Step 2: Calculate the interest earned
The interest earned on the investment can be calculated using the formula:
[tex]\[ \text{Interest Earned} = \text{Amount Invested} \times \text{Interest Rate} \times \left(\frac{\text{Days Invested}}{\text{Days in Year}}\right) \][/tex]
Substitute the known values:
[tex]\[ \text{Interest Earned} = 11,000 \times 0.023 \times \left(\frac{91}{360}\right) \][/tex]
When you perform this calculation, you get:
[tex]\[ \text{Interest Earned} = 63.95 \][/tex]
(rounded to two decimal places, this intermediate value will be more precisely calculated as seen in the final steps)
### Step 3: Calculate the yield
The yield can be calculated using the formula:
[tex]\[ \text{Yield Percent} = \left( \frac{\text{Interest Earned}}{\text{Amount Invested} + \text{Commission}} \right) \times 100 \% \][/tex]
We already have the following values:
- Interest Earned: Approximately \[tex]$63.95
- Amount Invested: \$[/tex]11,000
- Commission: \$20
Substituting these values into the yield formula gives:
[tex]\[ \text{Yield Percent} = \left( \frac{63.95}{11,000 + 20} \right) \times 100 \% \][/tex]
[tex]\[ \text{Yield Percent} = \left( \frac{63.95}{11,020} \right) \times 100 \% \][/tex]
Perform the division and multiplication:
[tex]\[ \text{Yield Percent} = 0.58 \% \][/tex]
### Step 4: Round the yield percentage to the nearest hundredth
The yield already calculated as 0.58% does not require additional rounding since it is given up to two decimal places.
So, the final answer is:
[tex]\[ \boxed{0.58\%} \][/tex]
This is the yield of the investment, rounded to the nearest hundredth.
