Question

The formula Upper S equals Upper C left parenthesis 1 plus r right parenthesis Superscript t models​ inflation, where Cequalsthe value​ today, requalsthe annual inflation rate​ (in decimal​ form), and Sequalsthe inflated value t years from now. If the inflation rate is 6​%, how much will a house now worth ​$73 comma 000 be worth in 6 ​years? Round your answer to the nearest dollar.
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Part 1
The house will be worth ​$
  
enter your response here. ​(Round to the nearest dollar as​ needed.)

Answer 1

To find the future value of the house given the current value, inflation rate, and the number of years, we can use the formula:

\[
S = C \times (1 + r)^t
\]

Where:
- \( S \) is the future value of the house.
- \( C \) is the current value of the house ($73,000).
- \( r \) is the annual inflation rate (6% or 0.06 in decimal form).
- \( t \) is the number of years (6 years).

Substituting the values into the formula:

1. Convert the percentages to decimal:
- \( r = 6\% = 0.06 \)

2. Plug in the values:
\[
S = 73000 \times (1 + 0.06)^6
\]

First calculate \( (1 + 0.06)^6 \):
\[
1 + 0.06 = 1.06
\]
Now raise it to the power of 6:
\[
1.06^6 \approx 1.418519
\]

3. Now calculate \( S \):
\[
S = 73000 \times 1.418519 \approx 103,853.79
\]

4. Round to the nearest dollar:
\[
S \approx 103,854
\]

The house will be worth approximately **$103,854** in 6 years.