The formula $S=C(1+r)^{t}$ models inflation, where $C=$ the value today, $r=$ the annual inflation rate (in decimal form), and $S=$ the inflated value t years from now. If the inflation rate is $6 \%$, how much will a house now worth $\$ 73,000$ be worth in 13 years? Round your answer to the nearest dollar.
Answer
Final Answer: The house will be worth \(\boxed{\$155704}\) in 13 years.
Step 1 ：Given that the formula for inflation is \(S=C(1+r)^{t}\), where \(C\) is the current value, \(r\) is the annual inflation rate in decimal form, and \(t\) is the number of years.
Step 2 ：We are given that \(C = \$73,000\), \(r = 6\% = 0.06\), and \(t = 13\) years.
Step 3 ：Substitute these values into the formula to find \(S\), the inflated value in 13 years.
Step 4 ：\(S = 73000(1+0.06)^{13}\)
Step 5 ：Calculate the value of \(S\) to find the inflated value of the house in 13 years.
Step 6 ：\(S = \$155704\)
Step 7 ：Final Answer: The house will be worth \(\boxed{\$155704}\) in 13 years.
