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 tyears from now. If the inflation rate is $$ 2 \% $$, how much will a house now worth $$ \$ 129,000 $$ be worth in 16 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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1. We begin with the inflation formula:  
   $$
   S = C(1+r)^t
   $$

2. The given values are:  
   $$
   C = 129\,000, \quad r = 0.02, \quad t = 16
   $$

3. Substitute these values into the formula:  
   $$
   S = 129\,000 \times (1 + 0.02)^{16}
   $$
   $$
   = 129\,000 \times (1.02)^{16}
   $$

4. Calculate $$(1.02)^{16}$$. Using a calculator, we find:  
   $$
   (1.02)^{16} \approx 1.373
   $$

5. Multiply to find $$ S $$:  
   $$
   S \approx 129\,000 \times 1.373 \approx 177\,117
   $$

6. Thus, rounding to the nearest dollar, the house will be worth:  
   $$
   \$177\,117
   $$
The house will be worth \$177,117 in 16 years.

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