①MIGGY RECEIVES A NOTE FOR $ 4,200 WHICH IS DUE IN ISO Days WITH INTEREST AT 6¼.% THE NOTE IS DISCOUNTED IMMEDIATELY at a Bank THAT CHARGES 6 ⅛% DISCOUNT. WHAT ARE THE PROCEEDS?

To solve this problem, we need to calculate the proceeds Miggy receives after discounting the note. Here’s how the process works:

1. **Step 1: Calculate the Bank Discount**
   - The bank discount formula is given by:

\[
\text{Bank Discount} = \text{Face Value} \times \text{Discount Rate} \times \frac{\text{Time}}{360}
\]

Where:
- The face value is \$4,200,
- The bank's discount rate is 6⅛% (6.125%),
- Time is 150 days (in banking, a year is typically treated as 360 days).

We first convert the rate into decimal form:

\[
6.125\% = 0.06125
\]

Now, plug in the values:

\[
\text{Bank Discount} = 4,200 \times 0.06125 \times \frac{150}{360}
\]

2. **Step 2: Subtract the Bank Discount from the Face Value to find the Proceeds**

\[
\text{Proceeds} = \text{Face Value} - \text{Bank Discount}
\]

Let’s compute this step-by-step:

### Step 1: Calculate Bank Discount

\[
\text{Bank Discount} = 4,200 \times 0.06125 \times \frac{150}{360}
\]

\[
\text{Bank Discount} = 4,200 \times 0.06125 \times 0.41667 \approx 107.33
\]

### Step 2: Calculate the Proceeds

\[
\text{Proceeds} = 4,200 - 107.33 = 4,092.67
\]

Thus, Miggy receives **\$4,092.67** as the proceeds.

Would you like a breakdown of any part of this process, or further details?

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Here are five related questions to extend your understanding:

1. How does the formula for calculating the bank discount change if the discount rate is compounded monthly?
2. What happens to the proceeds if the number of days is reduced?
3. How is the formula affected if the interest rate on the note increases to 7%?
4. How would the discount be computed if the note was not discounted immediately, but after 50 days?
5. What is the difference between discounting a note and earning interest on a loan?

**Tip:** Always ensure the time period is adjusted according to the bank's convention, which often treats a year as 360 days.

MIGGY RECEIVES A NOTE FOR $4,200 WHICH IS DUE IN 150 Days WITH INTEREST AT 6¼%. THE NOTE IS DISCOUNTED IMMEDIATELY at a Bank THAT CHARGES 6 ⅛% DISCOUNT. WHAT ARE THE PROCEEDS?

Learn how to calculate the proceeds from discounting a $4,200 note at 6.125% for 150 days. This problem covers key financial mathematics concepts like the bank discount formula and proceeds calculation, suitable for high school students in Grades 10-12.

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