The formula 

Upper S equals Upper C left parenthesis 1 plus r right parenthesis Superscript tS=C(1+r)t 

models​ inflation, where 

Cequals=the 

value​ today, 

requals=the 

annual inflation rate​ (in decimal​ form), and 

Sequals=the 

inflated value t years from now.  If the inflation rate is 

66​%, 

how much will a house now worth 

​$125 comma 000125,000 

be worth in 

2222 

​years? Round your answer to the nearest dollar.

To calculate the inflated value of the house in 22 years using the given formula $ S = C (1 + r)^t $:

- $ C $ is the current value of the house, which is \$125,000.
- $ r $ is the annual inflation rate in decimal form, which is 66% or 0.66.
- $ t $ is the number of years, which is 22.

Substitute the values into the formula:

\[ S = 125000 (1 + 0.66)^{22} \]

First, calculate $ 1 + 0.66 $:

\[ 1 + 0.66 = 1.66 \]

Next, raise 1.66 to the power of 22:

\[ 1.66^{22} \approx 1844.2 \]

Finally, multiply 125000 by 1844.2:

\[ S = 125000 \times 1844.2 \approx 230525000 \]

Rounding to the nearest dollar:

\[ S \approx 230525000 \]

So, the house will be worth approximately \$230,525,000 in 22 years.

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

1. How do you use a calculator to compute large exponents?
2. Can you explain why the inflated value grows so rapidly with a high inflation rate?
3. How does the compounding period affect the future value in inflation calculations?
4. Are there practical limits to using this formula in real-world scenarios?
5. How can you adjust the formula if the inflation rate varies year to year?

**Tip:** When working with high inflation rates over long periods, the future value can grow very quickly due to the compounding effect. Always double-check calculations to ensure accuracy.

Learn how to calculate the future value of an asset using the inflation rate of 66%. This problem involves exponential growth and compound interest concepts. Get a detailed step-by-step solution and understand how high inflation rates impact future values. Suitable for students in Grades 10-12.

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