Question 1172543: 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 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.
Calculate the exact day the note should be discounted to meet Richie's goal.
Answer by CPhill(1959)   (Show Source):
You can put this solution on YOUR website! Absolutely, let's break down this problem step-by-step.
**1. Calculate the Maturity Value of the Note**
* Principal (P): $800,000
* Interest Rate (R): 8.6% or 0.086
* Time (T): 90/360 (ordinary interest)
* Interest = P * R * T = $800,000 * 0.086 * (90/360) = $17,200
* Maturity Value (MV) = Principal + Interest = $800,000 + $17,200 = $817,200
**2. Calculate the Bank Discount for Different Days**
* Discount Rate (d): 13% or 0.13
* Time remaining (t) = (90-days)/360
* Bank Discount (BD) = MV * d * t
* Proceeds (PR) = MV - BD
* **Day 20:**
* Time remaining = (90 - 20) / 360 = 70 / 360
* BD = $817,200 * 0.13 * (70 / 360) = $20,601.33
* PR = $817,200 - $20,601.33 = $796,598.67
* Too high. Proceeds are less than $800,000.
* **Day 30:**
* Time remaining = (90 - 30) / 360 = 60 / 360
* BD = $817,200 * 0.13 * (60 / 360) = $17,762.67
* PR = $817,200 - $17,762.67 = $799,437.33
* Too high. Proceeds are less than $800,000.
* **Day 40:**
* Time remaining = (90 - 40) / 360 = 50 / 360
* BD = $817,200 * 0.13 * (50 / 360) = $14,802.22
* PR = $817,200 - $14,802.22 = $802,397.78
* Low enough. Proceeds are greater than $800,000.
**3. Calculate the Exact Day**
* We need to find the day when the proceeds are exactly $800,000.
* $800,000 = $817,200 - BD
* BD = $17,200
* $17,200 = $817,200 * 0.13 * t
* t = $17,200 / ($817,200 * 0.13)
* t = 0.1618333 (approximately)
* t * 360 = 58.26 days remaining.
* 90 - 58.26 = 31.74 days into the note.
Therefore, the bank discount on:
* Day 20: $20,601.33 (Too high)
* Day 30: $17,762.67 (Too high)
* Day 40: $14,802.22 (Low enough)
And Richie should discount the note on the 32nd day (rounding 31.74 up) to meet his goal.
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