Let’s break down the problem step-by-step:

Problem Analysis

The original price of the parking permit last year was $50, and it increased by 5% this year. We need to find:

1. The new price after this year’s 5% increase.
2. The price if it increases by another 5% next year.
3. Whether the parking permit price increased by the same amount each year.

Solution

Part (a): This Year’s Price

To calculate a 5% increase on $50:

• Formula: New Price = Original Price × (1 + Percentage Increase)
• Substitute values: $50 \times (1 + 0.05) = 50 \times 1.05 = 52.50$

Answer for (a): The price this year is $52.50.

Part (b): Next Year’s Price

Now, let’s calculate the price if it increases by another 5% next year based on this year’s price:

• New Price Next Year = Current Price × (1 + Percentage Increase)
• Substitute values: $52.50 \times 1.05 = 55.125$

Answer for (b): The price next year would be $55.13 (rounded to two decimal places).

Part (c): Did the Price Increase by the Same Amount?

Since each year's increase is based on 5% of the current price, the amount of increase changes each year. For example:

• This year’s increase was $50 \times 0.05 = 2.50$.
• Next year’s increase would be $52.50 \times 0.05 = 2.625$, which is different from this year’s increase.

Answer for (c): No, the parking permit did not increase by the same dollar amount each year, even though the percentage increase was the same.

Would you like further details on this solution or have any questions?

Follow-up Questions

1. How would the price change if the increase were 10% instead of 5% each year?
2. What would the price be after five years of 5% annual increases?
3. Can you calculate the compounded percentage increase over two years?
4. What is the difference between a fixed dollar increase and a percentage-based increase?
5. How would you calculate the price if the percentage change varied each year?

Tip

When dealing with percentage increases, multiplying by $1 + \text{rate}$ makes it easy to find compounded values over multiple years.