\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}
Real Tutor Solution
Answer
Solution
Reviewed and approved by the UpStudy tutoring team
Explain 
Simplify this solution The Deep Dive
To find the simple interest (SI) that Roger earned from the loan, we use the formula: \[ \text{SI} = P \times r \times t \] where \( P \) is the principal amount, \( r \) is the interest rate, and \( t \) is the time in years. Roger loaned Rafael \( \$25,000 \) at a rate of \( 7.25\% \) for \( 120 \) days. First, convert \( 120 \) days into years: \[ t = \frac{120}{365} \approx 0.329 \] So, \[ \text{SI} = 25000 \times 0.0725 \times 0.329 \approx 606.25 \] Therefore, the total interest earned by Roger from the loan is approximately \( \$606.25 \). Now, let's work out what simple interest rate Roger effectively earned when he sold the note to Novak at \( 8.25\% \) simple discount. The discount on the note can also be calculated, but we can now say that Roger has effectively sold the note at a higher interest noted, thus benefiting from the higher interest environment. Roger’s earnings from the interest and the discount’s impact create a fascinating illustration of how the bond market can fluctuate and how sales can work advantageously from simple fundamentals of lending. Furthermore, consider how higher interest rates impact the bond market; they generally lead to declining bond prices, but if you are strategically buying and selling, you might find immense opportunities where the numbers tell a compelling story of growth and profit!
