The value of your house, not including the lot, is \( \$ 91,000 \) today. What was the original cost if it had depreciated 5 percent per year for the past seven years?

To find the original cost of the house, we can use the formula for depreciation, which is given by: \[ V = P(1 - r)^t \] where \( V \) is the current value (\$91,000), \( P \) is the original price, \( r \) is the depreciation rate (5% or 0.05), and \( t \) is the number of years (7). Rearranging the formula to solve for \( P \): \[ P = \frac{V}{(1 - r)^t} \] Substituting the known values: \[ P = \frac{91,000}{(1 - 0.05)^7} = \frac{91,000}{(0.95)^7} \approx \frac{91,000}{0.674} \approx 135,000 \] So, the original cost of the house was approximately **\$135,000**. Understanding the impact of depreciation is crucial for homeowners, especially when considering selling or refinancing. Real estate often seems like a stable investment, but fluctuations in value, like a 5% annual depreciation, can significantly impact your net worth over time. It serves as a reminder to maintain your property’s value through repairs and updates! When calculating depreciation, a common mistake is to overlook the compound nature of the process. Instead of simply subtracting a percentage from the value, it’s essential to understand that each year you are applying that percentage to the remaining balance, not the original amount. Keeping your calculations lined up with the formula will ensure you avoid mishaps that can lead to inaccurate assessments.