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.)

To find the inflated value of the house in 22 years, we can plug the values into the given formula \( S = C(1 + r)^{t} \). Here, \( C = 66,000 \), \( r = 0.04 \), and \( t = 22 \). First, calculate \( (1 + r)^{t} \): \[ (1 + 0.04)^{22} = (1.04)^{22} \] Using a calculator, we find: \[ (1.04)^{22} \approx 2.3304 \] Now we can calculate \( S \): \[ S = 66,000 \times 2.3304 \approx 153,988.40 \] Rounding to the nearest dollar, the house will be worth \( \$ 153,988 \) in 22 years.