XYZ Corporation invests $$ \$ 10,000 $$ into 91-day treasury bills with an interest rate of $$ 2.5 \% $$. If the broker charges a $$ \$ 20 $$ commission, what is the yield? yield = [?]\% $$ \text { yield }=\frac{\text { amount invested (interest rate) }\left(\frac{\text { days invested }}{360 \text { days }}\right)}{\text { amount invested }\left(\frac{\text { days invested }}{360 \text { days }}\right)+\text { commission }} $$ Give your answer as a percent rounded to the nearest hundredth

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**Paso 1: Determinar los datos**

- Inversión principal: $$ P = \$10,\!000 $$
- Tasa de interés anual: $$ r = 2.5\% = 0.025 $$
- Días de inversión: $$ d = 91 $$ días
- Comisión del corredor: $$ C = \$20 $$

**Paso 2: Calcular la fracción del año para 91 días**

$$
\frac{d}{360} = \frac{91}{360}
$$

**Paso 3: Calcular el interés ganado sin considerar la comisión**

El interés ganado se calcula como:

$$
\text{Interés} = P \cdot r \cdot \frac{d}{360} = 10,\!000 \times 0.025 \times \frac{91}{360}
$$

Calculamos $$ 10,\!000 \times 0.025 $$:

$$
10,\!000 \times 0.025 = 250
$$

Entonces:

$$
\text{Interés} = 250 \times \frac{91}{360} = \frac{22750}{360} \approx 63.1944
$$

**Paso 4: Calcular la cantidad invertida ajustada al período**

La cantidad invertida proporcional a 91 días es:

$$
P \cdot \frac{d}{360} = 10,\!000 \times \frac{91}{360} = \frac{910000}{360} \approx 2527.7778
$$

**Paso 5: Aplicar la fórmula del rendimiento**

La fórmula del rendimiento es:

$$
\text{Rendimiento} = \frac{\text{Interés}}{P \cdot \frac{d}{360} + C}
$$

Sustituyendo los valores obtenidos:

$$
\text{Rendimiento} = \frac{63.1944}{2527.7778 + 20} = \frac{63.1944}{2547.7778}
$$

**Paso 6: Calcular el rendimiento**

Realizamos la división:

$$
\text{Rendimiento} \approx \frac{63.1944}{2547.7778} \approx 0.0248
$$

Para expresarlo en porcentaje:

$$
0.0248 \times 100 \approx 2.48\%
$$

**Respuesta final:** El rendimiento es de aproximadamente $$ \boxed{2.48\%} $$.
El rendimiento es de aproximadamente **2.48%**.

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

Give your answer as a percent rounded to the nearest hundredth

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XYZ Corporation invests into 91-day treasury bills with an interest rate of . If the broker charges a commission, what is the yield? yield = [?]% Give your answer as a percent rounded to the nearest hundredth