A frozen pizza that originally sold for 4.85 undergoes a 5% price increase each year.
(a) Find the new cost of the frozen pizza after 11 years. Round your answer to the nearest cent.
The new cost of the frozen pizza after 11 years is $?

To find the new cost of the frozen pizza after 11 years, we need to apply the formula for compound interest since the price is increasing by a fixed percentage each year.

The formula for the price after $ n $ years with a fixed annual increase is given by:

\[
P_n = P_0 \times (1 + r)^n
\]

where:
- $ P_n $ is the price after $ n $ years,
- $ P_0 $ is the original price,
- $ r $ is the annual rate of increase (as a decimal),
- $ n $ is the number of years.

Given:
- $ P_0 = 4.85 $ (the original price),
- $ r = 5\% = 0.05 $,
- $ n = 11 $ years.

Substituting these values into the formula:

\[
P_{11} = 4.85 \times (1 + 0.05)^{11}
\]

\[
P_{11} = 4.85 \times (1.05)^{11}
\]

Now let's calculate the value of $ (1.05)^{11} $ and then multiply it by 4.85 to find the new cost.

\[
(1.05)^{11} \approx 1.71034
\]

\[
P_{11} = 4.85 \times 1.71034 \approx 8.29514
\]

Rounding to the nearest cent, the new cost of the frozen pizza after 11 years is approximately **$8.30**.

Would you like more details or have any questions? Here are some related questions:

1. What would the price be after 15 years?
2. How much total price increase does the pizza undergo over the 11 years?
3. What is the percentage increase in price from the original to the 11-year mark?
4. If the rate of increase were 6% instead of 5%, what would the price be after 11 years?
5. How does the final price change if the increase happens semi-annually instead of annually?

**Tip:** Compound interest, even with small percentages, can lead to significant growth over time, demonstrating the power of exponential functions in finance.

Learn how to calculate the new cost of a frozen pizza after 11 years with a 5% annual price increase using compound interest formula. Understand the impact of exponential growth on prices over time. Suitable for high school students and beyond.

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