Question: On April 5, 2022, Janeen Camoct took out an 8.5% loan for $20,000. The loan is due March 9, 2023. Janeen's terms are ordinary interest. Sabrina Bowers took out the same loan as Janeen. Sabrina’s terms, however, are exact interest. (Ignore leap year.) (Use Days in a year table (opens in a new tab).)\n\nRequired:\nWhat is Sabrina’s difference in interest?\n\nNote: Do not round intermediate calculations. Round your answer to the nearest cent.\n\nWhat will Sabrina pay on March 9, 2023?\n\nNote: Round your answer to the nearest cent.
1. **State the problem:** Calculate the difference in interest Sabrina pays compared to Janeen, and find the total amount Sabrina will pay on March 9, 2023, given an 8.5% loan of $20,000 from April 5, 2022, to March 9, 2023, with ordinary and exact interest methods respectively.\n\n2. **Identify formulas and rules:**\n- Ordinary interest uses 360 days per year.\n- Exact interest uses 365 days per year.\n- Interest formula: $$I = P \times r \times t$$ where $P$ is principal, $r$ is annual interest rate (decimal), and $t$ is time in years.\n\n3. **Calculate the time period in days:**\n- From April 5, 2022, to March 9, 2023.\n- Count days for ordinary interest (360-day year) and exact interest (365-day year).\n\n4. **Calculate days between dates:**\n- April 5 to April 30: $30 - 5 = 25$ days\n- May: 31 days\n- June: 30 days\n- July: 31 days\n- August: 31 days\n- September: 30 days\n- October: 31 days\n- November: 30 days\n- December: 31 days\n- January 2023: 31 days\n- February 2023: 28 days (not leap year)\n- March 1 to March 9: 9 days\n\nTotal days = $25 + 31 + 30 + 31 + 31 + 30 + 31 + 30 + 31 + 31 + 28 + 9 = 338$ days\n\n5. **Calculate time in years for each method:**\n- Ordinary interest time: $$t_o = \frac{338}{360} = 0.938888\ldots$$\n- Exact interest time: $$t_e = \frac{338}{365} = 0.926027\ldots$$\n\n6. **Calculate interest for Janeen (ordinary interest):**\n$$I_o = 20000 \times 0.085 \times 0.938888 = 1596.11$$ (rounded to 2 decimals)\n\n7. **Calculate interest for Sabrina (exact interest):**\n$$I_e = 20000 \times 0.085 \times 0.926027 = 1574.14$$ (rounded to 2 decimals)\n\n8. **Calculate difference in interest:**\n$$\text{Difference} = I_o - I_e = 1596.11 - 1574.14 = 21.97$$\n\n9. **Calculate total amount Sabrina will pay:**\n$$\text{Total} = P + I_e = 20000 + 1574.14 = 21574.14$$\n\n**Final answers:**\n- Sabrina’s difference in interest is $21.97$.\n- Sabrina will pay $21574.14$ on March 9, 2023.