\begin{tabular}{l} Secondary Sales: The Bond Market \\ Roger loaned Rafael \( \$ 25,000 \) for 120 days at \( 7.25 \% \) simple interest. \\ 30 days later he sold the note to Novak, at an \( 8.25 \% \) simple discount \\ rate. \\ rameric 1 point \\ What simple interest rate did Roger earn from the loan? \\ \hline\end{tabular}

To determine the effective simple interest rate that Roger earned from the loan after selling the note to Novak, follow these steps: 1. **Initial Loan Details:** - **Principal (P):** \$25,000 - **Interest Rate (r₁):** 7.25% per annum - **Loan Duration:** 120 days 2. **Interest Earned in the First 30 Days:** \[ \text{Interest}_1 = P \times r₁ \times \frac{t}{360} = 25,000 \times 0.0725 \times \frac{30}{360} = \$151.04 \] - **Total Amount After 30 Days:** \$25,151.04 3. **Selling the Note to Novak:** - **Remaining Duration:** 90 days - **Discount Rate (d):** 8.25% per annum The present value (PV) of the remaining amount using simple discount: \[ \text{PV} = \frac{F}{1 + d \times \frac{t}{360}} = \frac{25,604.17}{1 + 0.0825 \times \frac{90}{360}} \approx \$25,076.98 \] 4. **Total Amount Received by Roger:** \[ \text{Total Received} = \text{Interest}_1 + \text{PV} = 151.04 + 25,076.98 = \$25,228.02 \] 5. **Calculating the Effective Interest Rate:** - **Total Interest Earned (I):** \$228.02 - **Effective Rate (r):** \[ r = \frac{I}{P \times \frac{t}{360}} = \frac{228.02}{25,000 \times \frac{120}{360}} = \frac{228.02}{8,333.33} \approx 0.0273 \text{ or } 2.73\% \] **Conclusion:** Roger effectively earned an approximate **2.73%** simple interest rate from the loan after selling the note. **Answer:** Roger earned an effective simple interest rate of approximately 2.73 %.