Answer:
To calculate the percent growth of the value of the house in ten years, we can use the compound interest formula:
A = P(1 + r/n)^(nt)
Where:
A = Final value of the house
P = Initial value of the house
r = Annual interest rate (as a decimal)
n = Number of times the interest is compounded per year
t = Number of years
In this case, the annual interest rate is 8% or 0.08, the number of times the interest is compounded per year is 1 (since it increases annually), and the number of years is 10.
Let's assume the initial value of the house is $100,000.
P = $100,000
r = 0.08
n = 1
t = 10
A = 100000(1 + 0.08/1)^(1*10)
A = 100000(1 + 0.08)^10
A ≈ 215,892.66
The final value of the house after ten years would be approximately $215,892.66.
To calculate the percent growth of the value, we can use the formula:
Percent Growth = ((A - P) / P) * 100
Percent Growth = ((215892.66 - 100000) / 100000) * 100
Percent Growth ≈ 115.89%
Therefore, the percent growth of the value of the house in ten years is approximately 115.89%.
To find the factor by which the value of the house grows every ten years, we can divide the final value by the initial value:
Factor = A / P
Factor ≈ 215892.66 / 100000
Factor ≈ 2.1589
Therefore, the value of the house grows by a factor of approximately 2.1589 every ten years.