Jay purchased a 180-day $500,000 bank bill (at a simple interest rate) on 16 July 2023. The purchase price was $490,550. He sold this bank bill on 12 August 2023.

(a) What was his selling price, if he sold this bank bill at a yield of 3.02% p.a. (simple interest)? Round your answer to three decimal places.

To solve for the selling price of the bank bill that Jay sold on 12 August 2023, we need to break down the problem into a few key steps. Here’s the process:

### Step 1: Calculate the number of days Jay held the bank bill.
- **Purchase Date:** 16 July 2023
- **Selling Date:** 12 August 2023

Calculate the number of days between these two dates:

- **16 July to 31 July:** 15 days (July has 31 days)
- **1 August to 12 August:** 12 days

Total days Jay held the bill = 15 + 12 = **27 days**

### Step 2: Determine the holding period yield (HPY).
The holding period yield (HPY) is the interest rate for the period Jay held the bank bill. It’s calculated using the annual yield rate and adjusting it for the 27-day period.

Given:
- Annual Yield Rate (simple interest): 3.02% p.a.
- Number of days held: 27
- Number of days in the year (assuming a 365-day year): 365

\[
\text{HPY} = \left(\frac{3.02\%}{365}\right) \times 27
\]

\[
\text{HPY} = \frac{3.02}{365} \times 27 = 0.0000827397 \times 27 = 0.002234
\]

### Step 3: Calculate the selling price of the bank bill.
The formula to calculate the selling price of a bank bill based on yield is:

\[
\text{Selling Price} = \frac{\text{Face Value}}{1 + \text{HPY}}
\]

Given:
- Face Value of the bank bill = $500,000
- HPY = 0.002234

\[
\text{Selling Price} = \frac{500,000}{1 + 0.002234} = \frac{500,000}{1.002234} = 498,886.365
\]

### Answer:
The selling price of the bank bill is **$498,886.365** (rounded to three decimal places).

Would you like more details or have any questions?

Here are 8 related questions for further exploration:
1. How is the holding period yield (HPY) affected by different yield rates?
2. What would be the impact on the selling price if the holding period was longer?
3. How do you calculate the annual yield rate from the selling price?
4. What is the relationship between the purchase price and the yield rate?
5. How does simple interest differ from compound interest in such financial calculations?
6. How would the result change if the number of days in the year was assumed to be 360 instead of 365?
7. What would Jay's profit or loss be from this transaction?
8. How do market conditions affect the yield rate at which the bank bill is sold?

**Tip:** Understanding the differences between simple and compound interest is crucial for accurately interpreting financial investments and their returns.

Learn how to calculate the selling price of a bank bill with a 3.02% annual yield rate using simple interest. Detailed step-by-step solution including calculation of holding period yield (HPY) and application of the selling price formula. Suitable for advanced high school students studying financial mathematics.

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