Final answer:
It will take approximately 23 years for the house value to reach $225,000.
Step-by-step explanation:
To find out approximately how many years it will take for the value of the house to reach $225,000, we need to calculate the number of periods it will take for the initial value of $125,000 to grow to $225,000 at a rate of 4% per year.
We can use the formula for compound interest: A = P(1 + r)^n, where A is the final amount, P is the initial amount, r is the rate, and n is the number of periods.
In this case, the initial amount is $125,000, the rate is 4% per year (or 0.04), and the final amount is $225,000. We need to solve for n. Rearranging the formula, we have: n = log1+r(A/P).
Using logarithms and plugging in the values, we get: n ≈ log1.04(225,000/125,000). Evaluating this expression gives us approximately 22.67 years. Rounding up, it will take approximately 23 years for the value of the house to reach $225,000.