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.