ANZ arranges financing for Super Duper Pty Ltd with a 90 day bank bill with a Face Value of $500,000.  City Investments buy the bill when it is first issued at a yield of 4.75% pa and sell it 30 days later to Prudential Investments at a yield of 4.55% pa. What price does City Investments pay for the bill?


Group of answer choices

$500,000.00

$494,452.65

$498,055.54

$496,126.14

$494,211.63

We are dealing with a bank bill, where the price can be calculated using the **yield** formula for a discount security. The formula is:

\[
P = \frac{F}{1 + \left( \frac{r \times t}{365} \right)}
\]

Where:
- $P$ is the price of the bill,
- $F$ is the face value of the bill,
- $r$ is the annual yield (as a decimal),
- $t$ is the time in days the bill is held,
- 365 is the number of days in a year (for bank bills, we typically assume a 365-day year).

### Step-by-Step Process:

1. **Face Value ($F$)** = $500,000
2. **Annual Yield ($r$)** = 4.75% pa = 0.0475
3. **Time to Maturity ($t$)** = 90 days (since it's a 90-day bill)

Now, plug these values into the formula:

\[
P = \frac{500,000}{1 + \left( \frac{0.0475 \times 90}{365} \right)}
\]

Let’s calculate that.

The price that City Investments pays for the bill is **$494,211.63**.

Would you like more details or have any questions? 

Here are five related questions to expand on this topic:
1. How is the yield of a financial instrument calculated?
2. What factors influence the price of a bank bill?
3. How does the time to maturity affect the price of a bill?
4. What is the difference between nominal and effective yield?
5. How do changes in interest rates affect bond prices?

**Tip**: For short-term investments like bank bills, the price moves inversely with changes in yield—the higher the yield, the lower the price.

ANZ arranges financing for Super Duper Pty Ltd with a 90 day bank bill with a Face Value of $500,000. City Investments buy the bill when it is first issued at a yield of 4.75% pa and sell it 30 days later to Prudential Investments at a yield of 4.55% pa. What price does City Investments pay for the bill?

Learn how to calculate the price that City Investments pays for a 90-day bank bill with a face value of $500,000. This finance problem involves yield calculation and demonstrates how changes in yield affect the price of a bank bill. Suitable for undergraduate finance students.

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