\( \square \) *Untitled - Notepad File Edit Format View Help \( \$ 2 \) Steve Perry borrowed \( \$ 50,000 \) at \( 12 \% \) ordinary interest for 60 days. On day 20 of the loan, Steve made a partial payment of \( \$ 7,000 \). What is the new maturity value (in \( \$ \) ) of the loan? (Round your answer to two decimal places.)

To find the new maturity value of the loan, we first need to calculate the interest for the initial 20 days on the original loan amount of \( \$ 50,000 \). The formula for ordinary interest is: \[ I = P \times r \times t \] where \( I \) is the interest, \( P \) is the principal, \( r \) is the rate (in decimal), and \( t \) is the time in years. Since we are using ordinary interest, we consider a 360-day year. 1. **Calculate the interest for the first 20 days:** - \( P = 50,000 \) - \( r = 0.12 \) - \( t = \frac{20}{360} \) \[ I = 50,000 \times 0.12 \times \frac{20}{360} = 50,000 \times 0.12 \times 0.05556 \approx 1,000 \] So, the interest for the first 20 days is approximately \( \$ 1,000 \). 2. **Calculate the new principal after the partial payment:** - Total owed after 20 days before payment is \( 50,000 + 1,000 = 51,000 \). - After the partial payment of \( 7,000 \), the new principal will be: \[ 51,000 - 7,000 = 44,000 \] 3. **Calculate the interest for the remaining 40 days:** - Now we calculate the interest on the new principal for the remaining 40 days. - \( P = 44,000 \) - \( t = \frac{40}{360} \) \[ I = 44,000 \times 0.12 \times \frac{40}{360} \approx 44,000 \times 0.12 \times 0.1111 \approx 588.89 \] 4. **Calculate the new maturity value:** - The new total amount owed will be the new principal plus the interest for the next 40 days. \[ Maturity Value = 44,000 + 588.89 \approx 44,588.89 \] So, rounding to two decimal places, the new maturity value of the loan is \( \$ 44,588.89 \).