To find the value of Jericho's house in 2019, we need to calculate the annual appreciation and add it to the initial value of $450,000.
The annual appreciation rate is 5%, which means the value of the house increases by 5% each year. To calculate the value of the house in 2019, we need to find the cumulative appreciation over the 10-year period from 2010 to 2019.
First, we calculate the appreciation for each year:
Year 1: 5% of $450,000 = $22,500
Year 2: 5% of ($450,000 + $22,500) = $23,625
Year 3: 5% of ($450,000 + $22,500 + $23,625) = $24,806.25
And so on, for each subsequent year.
We can simplify the calculation by using the formula for the future value of a present sum with continuous compounding:
Future Value = Present Value × (1 + Rate)^n
Using this formula, we can calculate the future value of the house in 2019:
Future Value = $450,000 × (1 + 0.05)^10
Calculating this expression gives us the value of Jericho's house in 2019:
Future Value = $450,000 × (1.05)^10 ≈ $450,000 × 1.62889 ≈ $732,000
Therefore, the value of Jericho's house in 2019 would be approximately $732,000.