\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. \\ numeric. 1 point \\ What was the maturity value of the original note? \\ Type your answer... \\ \hline\end{tabular}

To find the maturity value of the original note that Roger loaned to Rafael, we can use the formula for simple interest: \[ I = P \times r \times t \] where: - \( I \) is the interest, - \( P \) is the principal amount (the initial loan), - \( r \) is the interest rate (as a decimal), - \( t \) is the time in years. ### Step 1: Calculate the interest 1. **Principal Amount (\( P \))**: \( 25,000 \) 2. **Interest Rate (\( r \))**: \( 7.25\% = 0.0725 \) 3. **Time (\( t \))**: \( 120 \) days, which is \( \frac{120}{360} \) years (using a 360-day year for simplicity in financial calculations). Now, we can calculate the interest: \[ t = \frac{120}{360} = \frac{1}{3} \text{ years} \] Now substituting the values into the interest formula: \[ I = 25000 \times 0.0725 \times \frac{1}{3} \] ### Step 2: Calculate the maturity value The maturity value (\( MV \)) is given by: \[ MV = P + I \] Now, let's calculate the interest and then the maturity value. I'll perform the calculations now. Calculate the value by following steps: - step0: Calculate: \(25000\times 0.0725\left(\frac{120}{360}\right)\) - step1: Reduce the fraction: \(25000\times 0.0725\times \frac{1}{3}\) - step2: Multiply the terms: \(1812.5\times \frac{1}{3}\) - step3: Convert the expressions: \(\frac{3625}{2}\times \frac{1}{3}\) - step4: Multiply the numbers: \(\frac{3625}{6}\) Calculate or simplify the expression \( 25000 + (25000 * 0.0725 * (120/360)) \). Calculate the value by following steps: - step0: Calculate: \(25000+\left(25000\times 0.0725\left(\frac{120}{360}\right)\right)\) - step1: Reduce the fraction: \(25000+\left(25000\times 0.0725\times \frac{1}{3}\right)\) - step2: Multiply the terms: \(25000+\frac{3625}{6}\) - step3: Reduce fractions to a common denominator: \(\frac{25000\times 6}{6}+\frac{3625}{6}\) - step4: Transform the expression: \(\frac{25000\times 6+3625}{6}\) - step5: Multiply the numbers: \(\frac{150000+3625}{6}\) - step6: Add the numbers: \(\frac{153625}{6}\) ### Step 1: Calculate the Interest The interest calculated is: \[ I = 25000 \times 0.0725 \times \frac{120}{360} = 604.1667 \text{ (approximately)} \] ### Step 2: Calculate the Maturity Value Now, we can find the maturity value: \[ MV = 25000 + 604.1667 = 25604.1667 \text{ (approximately)} \] ### Final Answer The maturity value of the original note is approximately: \[ \text{Maturity Value} \approx 25604.17 \] Thus, the maturity value of the original note is **$25,604.17**.