The formula Upper S equals Upper C left parenthesis 1 plus r right parenthesis Superscript t models​ inflation, where Cequalsthe value​ today, requalsthe annual inflation rate​ (in decimal​ form), and Sequalsthe inflated value t years from now.  If the inflation rate is 2​%, how much will a house now worth ​$58 comma 000 be worth in 11 ​years? Round your answer to the nearest dollar.

To calculate the inflated value of the house in 11 years using the given formula $ S = C (1 + r)^t $:

- $ C $ is the current value of the house, which is \$58,000.
- $ r $ is the annual inflation rate in decimal form, which is 2% or 0.02.
- $ t $ is the number of years, which is 11.

Substitute the values into the formula:

\[ S = 58000 (1 + 0.02)^{11} \]

First, calculate $ 1 + 0.02 $:

\[ 1 + 0.02 = 1.02 \]

Next, raise 1.02 to the power of 11:

\[ 1.02^{11} \approx 1.2434 \]

Finally, multiply 58000 by 1.2434:

\[ S = 58000 \times 1.2434 \approx 72117.2 \]

Rounding to the nearest dollar:

\[ S \approx 72117 \]

So, the house will be worth approximately \$72,117 in 11 years.

Would you like more details or have any questions? Here are 5 questions you might ask next:

1. How do you convert a percentage into a decimal form for calculations?
2. Can you explain the steps to raise a number to a power?
3. What are some common uses of the compound interest formula?
4. How does changing the inflation rate affect the future value?
5. What other factors should be considered when calculating future house values?

**Tip:** Always ensure you convert percentages to decimal form before using them in mathematical formulas. For example, 5% becomes 0.05.

Learn how to calculate the future value of a house considering inflation. Using the compound interest formula, find out how much a house worth $58,000 today will be worth in 11 years with an inflation rate of 2%. Detailed step-by-step solution provided.

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