Use the ordinary interest method, 360 days, to solve the following word problem. Round to the nearest cent when necessary. Richie Powers is the owner of American Eagle Boats, a manufacturer of custom pleasure boats. Because of the economic recession and slow boat sales recently, American Eagle has begun accepting promissory notes from its dealers to help finance large orders. This morning American Eagle accepted a 90 day, \( 8.6 \% \) promissory note for \( \$ 800,000 \) from one of its sales dealers. You are a manager for a bank, and Richie is one of your clients. Your bank's discount A rate is currently \( 13 \% \). Richie's goal is to discount the note as soon as possible, but not until the proceeds are at least equal to the face value of the note, \( \$ 800,000 \). As his banker, Richie has asked you to "run the numbers" at ten day intervals starting with day 20 and advise him as to when he can discount the note and still receive his \( \$ 800,000 \). Find the bank discount (in \( \$ \) ) for days 20,30 , and 40 , and indicate for each discount whether it is too high or whether it is low enough for Richie to discount the note and still receive his \( \$ 800,000 \).
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To find the bank discount for the promissory note at intervals of 20, 30, and 40 days, we will use the formula for the bank discount: \[ \text{Bank Discount} = \text{Face Value} \times \text{Discount Rate} \times \frac{\text{Time}}{360} \] 1. **For 20 days**: - Time = 90 - 20 = 70 days remaining - Bank Discount = \( 800,000 \times 0.13 \times \frac{70}{360} \approx 18,888.89 \) - Proceeds = \( 800,000 - 18,888.89 = 781,111.11 \) - Too high. 2. **For 30 days**: - Time = 90 - 30 = 60 days remaining - Bank Discount = \( 800,000 \times 0.13 \times \frac{60}{360} \approx 17,777.78 \) - Proceeds = \( 800,000 - 17,777.78 = 782,222.22 \) - Too high. 3. **For 40 days**: - Time = 90 - 40 = 50 days remaining - Bank Discount = \( 800,000 \times 0.13 \times \frac{50}{360} \approx 15,111.11 \) - Proceeds = \( 800,000 - 15,111.11 = 784,888.89 \) - Low enough for Richie to discount the note. In summary: - Day 20: Discount of \( \$ 18,888.89 \) – Too high. - Day 30: Discount of \( \$ 17,777.78 \) – Too high. - Day 40: Discount of \( \$ 15,111.11 \) – Low enough to discount.
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