The formula \( \mathrm{S}=\mathrm{C}(1+r)^{\prime} \) models inflation, where \( \mathrm{C}= \) the value loday, \( \mathrm{r}= \) the annual inllation rale (in decimal form), and \( \mathrm{S}= \) the inflated value \( t \) years from now. If the fllation rate is \( 5 \% \), how much will a house now worth \( \$ 200,000 \) be worth in 15 years? Round your answer to the nearest dollar. The house will be worth \( \$ \square \). (Round to the nearest dollar as needed.)

To calculate the future value of a house worth $200,000 in 15 years with an annual inflation rate of 5%, we can use the formula \( S = C(1 + r)^{t} \). Here, \( C = 200,000 \), \( r = 0.05 \), and \( t = 15 \). Plugging in the values: \[ S = 200,000(1 + 0.05)^{15} \] \[ S = 200,000(1.05)^{15} \] Calculating \( (1.05)^{15} \): \[ (1.05)^{15} \approx 2.07893 \] Now substitute back: \[ S \approx 200,000 \times 2.07893 \approx 415,786 \] Thus, the house will be worth approximately \( \$ 415,786 \) in 15 years when rounded to the nearest dollar. The house will be worth \( \$ 415,786 \).