Questions: XYZ Corporation invests 5,000 into 91-day treasury bills with an interest rate of 2.5 %. If the broker charges a 30 commission, what is the yield? yield = [?]%

Solution Steps

To find the yield, we need to calculate the interest earned from the treasury bills and then subtract the commission to find the net gain. The yield is then the net gain divided by the initial investment, expressed as a percentage.

1. Calculate the interest earned using the formula: \[ \text{Interest} = \text{Principal} \times \left(\frac{\text{Rate}}{100}\right) \times \left(\frac{\text{Days}}{365}\right) \] where Principal is \$5,000, Rate is 2.5%, and Days is 91.

2. Subtract the commission from the interest to get the net gain.

3. Calculate the yield as: \[ \text{Yield} = \left(\frac{\text{Net Gain}}{\text{Principal}}\right) \times 100 \]

The interest earned from the treasury bills is calculated using the formula: \[ \text{Interest} = P \times \left(\frac{r}{100}\right) \times \left(\frac{d}{365}\right) \] Substituting the values: \[ \text{Interest} = 5000 \times \left(\frac{2.5}{100}\right) \times \left(\frac{91}{365}\right} \approx 31.1644 \]

The net gain is found by subtracting the broker's commission from the interest: \[ \text{Net Gain} = \text{Interest} - \text{Commission} = 31.1644 - 30 = 1.1644 \]

The yield is calculated as: \[ \text{Yield} = \left(\frac{\text{Net Gain}}{P}\right) \times 100 \] Substituting the values: \[ \text{Yield} = \left(\frac{1.1644}{5000}\right) \times 100 \approx 0.0233 \]

Final Answer