To determine how much Jen will receive for her house after 5 years, considering an average annual inflation rate of 3%, we can use the compound interest formula, which accounts for the effects of inflation on the value of the house over time.
The formula for calculating the future value with inflation taken into account is:
[tex]\[ \text{Future Value} = \text{Present Value} \times (1 + \text{Inflation Rate})^t \][/tex]
Here, the present value is the initial purchase price of the house, the inflation rate is the annual average rate of inflation, and [tex]\( t \)[/tex] is the number of years into the future.
Given:
- Present Value (purchase price) = [tex]$250,000$[/tex]
- Inflation Rate = 3% or 0.03
- Time Period [tex]\( t \)[/tex] = 5 years
We substitute these values into the formula:
[tex]\[ \text{Future Value} = 250,000 \times (1 + 0.03)^5 \][/tex]
First, we calculate [tex]\( 1 + 0.03 \)[/tex]:
[tex]\[ 1 + 0.03 = 1.03 \][/tex]
Next, we raise 1.03 to the power of 5:
[tex]\[ 1.03^5 \approx 1.159274 \][/tex]
Now, we multiply this result by the initial purchase price:
[tex]\[ 250,000 \times 1.159274 \approx 289,818.52 \][/tex]
So, Jen will receive approximately [tex]$289,818.52$[/tex] if she sells her house after 5 years with an average annual inflation rate of 3%.
