The formula $$ \mathrm{S}=\mathrm{C}(1+r)^{t} $$ models inflation, where $$ \mathrm{C}= $$ the value today, $$ \mathrm{r}= $$ the annual inflation rate (in decimal form), and $$ \mathrm{S}= $$ the inflated value t years from now. If the inflation rate is $$ 4 \% $$, how much will a house now worth $$ \$ 66,000 $$ be worth in 22 years? Round your answer to the nearest dollar. The house will be worth $$ \$ \square $$. (Round to the nearest dollar as needed.)

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Given the formula for inflation $$ S = C(1 + r)^t $$, where:
- $$ C $$ is the value today,
- $$ r $$ is the annual inflation rate in decimal form,
- $$ S $$ is the inflated value t years from now.

We are given:
- The inflation rate $$ r = 4\% = 0.04 $$ (in decimal form),
- The value today $$ C = \$66,000 $$,
- The number of years $$ t = 22 $$.

We need to find the inflated value of the house in 22 years.

Substitute the given values into the formula:
$$ S = 66000(1 + 0.04)^{22} $$

Now, we can calculate the inflated value of the house in 22 years.
Calculate the value by following steps:
- step0: Calculate:
  $$66000\left(1+0.04\right)^{22}$$
- step1: Add the numbers:
  $$66000\times 1.04^{22}$$
- step2: Convert the expressions:
  $$66000\left(\frac{26}{25}\right)^{22}$$
- step3: Simplify:
  $$66000\times \frac{26^{22}}{25^{22}}$$
- step4: Rewrite the expression:
  $$125\times 528\times \frac{26^{22}}{25^{22}}$$
- step5: Rewrite the expression:
  $$5^{3}\times 528\times \frac{26^{22}}{5^{44}}$$
- step6: Reduce the numbers:
  $$528\times \frac{26^{22}}{5^{41}}$$
- step7: Multiply:
  $$\frac{528\times 26^{22}}{5^{41}}$$
The inflated value of the house in 22 years will be approximately $156,414.64.

Rounding to the nearest dollar, the house will be worth $156,415 in 22 years.
The house will be worth \$156,415 in 22 years.

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