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Math  /  Algebra

QuestionProceeds from Notes Payable On May 15, Franklin Co. borrowed cash from Dakota Bank by issuing a 90 -day note with a face amount of $180,000\$ 180,000. Assume a 360 -day year. Required: a. Determine the proceeds of the note, assuming that the note carries an interest rate of 8%8 \%.
5 □\square b. Determine the proceeds of the note, assuming that the note is discounted at 8%8 \%. \ \square$

Studdy Solution

STEP 1

What is this asking? We need to figure out how much money Franklin Co. actually gets from Dakota Bank after taking out a loan, considering two different scenarios: one where they pay interest separately and one where the interest is taken out upfront. Watch out! Don't mix up the **face value** of the note (the amount written on it) with the **proceeds** (the actual cash received).
Also, make sure to use the correct number of days in the year (**360**) as stated in the problem.

STEP 2

1. Calculate proceeds with separate interest
2. Calculate proceeds with discounted interest

STEP 3

Let's **define** what "proceeds" means in this context.
Proceeds are the actual amount of cash Franklin Co. receives. When the interest is paid separately, the proceeds are simply equal to the **face value** of the note.

STEP 4

So, in this case, the proceeds are $180,000\$180,000.
Easy peasy!

STEP 5

Now, things get a little more interesting!
With a **discounted note**, the interest is subtracted *upfront*.
This means Franklin Co. receives less than the face value initially.

STEP 6

**Calculate the interest:** The interest is calculated on the **face value** for the **duration** of the loan.
The formula for simple interest is Interest=Principal⋅Rate⋅Time \text{Interest} = \text{Principal} \cdot \text{Rate} \cdot \text{Time} .

STEP 7

Let's **plug in** our values: Interest=$180,000⋅0.08⋅90360\text{Interest} = \$180,000 \cdot 0.08 \cdot \frac{90}{360}

STEP 8

**Simplify the fraction**: 90/36090/360 simplifies to 1/41/4 because 90⋅4=36090 \cdot 4 = 360.
So we divide both the numerator and denominator by 90 to get 1/41/4.

STEP 9

**Calculate the interest:** Interest=$180,000⋅0.08⋅14=$3,600\text{Interest} = \$180,000 \cdot 0.08 \cdot \frac{1}{4} = \$3,600

STEP 10

**Calculate the proceeds:** The proceeds are the **face value** *minus* the **interest**.

STEP 11

Proceeds=$180,000−$3,600=$176,400\text{Proceeds} = \$180,000 - \$3,600 = \$176,400

STEP 12

a. Proceeds with separate interest: $180,000\$180,000 b. Proceeds with discounted interest: $176,400\$176,400

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