Let's use the formula [tex]\( S = C (1+ r )^{ t } \)[/tex] to determine the inflated value of the house in 19 years given the parameters provided.
1. Identify the variables in the given problem:
- Current value (C): \[tex]$196,000
- Annual inflation rate (r): 7%, which should be converted to a decimal, so \( r = 0.07 \)
- Number of years (t): 19
2. Substitute the values into the formula:
\[
S = 196,000 \times (1 + 0.07)^{19}
\]
3. Calculate the expression inside the parentheses first:
\[
1 + 0.07 = 1.07
\]
4. Raise this number to the power of 19 (the number of years):
\[
1.07^{19}
\]
5. Multiply the result by the current value of the house (\$[/tex]196,000):
[tex]\[
S = 196,000 \times 1.07^{19}
\][/tex]
6. Perform the final multiplication to find the inflated value.
7. Round the result to the nearest dollar to get the final answer.
After following these steps, the future value of the house is approximately \$708,839.
