Say that you purchase a house for $150,000 by getting a mortgage for $135,000 and paying a $15,000 down payment. Assume you get a 15-year mortgage with a 6 percent interest rate. If the house appreciates at a 2 percent rate per year, what will be the value of the house in seven years? How much of this value is equity?
To calculate the value of the house in seven years, we need to consider both the initial purchase price and the rate of appreciation.
First, let's determine the annual appreciation of the house. The house appreciates at a rate of 2 percent per year, so we can calculate the appreciation amount for each year using the formula:
Appreciation = Initial Value * Appreciation Rate
In this case, the initial value of the house is $150,000. Therefore, the appreciation amount for each year is:
Year 1: $150,000 * 0.02 = $3,000
Year 2: $153,000 * 0.02 = $3,060
Year 3: $156,060 * 0.02 = $3,121.20
Year 4: $159,181.20 * 0.02 = $3,183.62
Year 5: $162,364.82 * 0.02 = $3,247.30
Year 6: $165,612.12 * 0.02 = $3,312.24
Year 7: $168,924.36 * 0.02 = $3,378.49
Next, let's calculate the value of the house in seven years. To do this, we add the total appreciation amount to the initial purchase price:
Value of House in 7 years = Initial Value + Total Appreciation Amount
Value of House in 7 years = $150,000 + ($3,000 + $3,060 + $3,121.20 + $3,183.62 + $3,247.30 + $3,312.24 + $3,378.49)
Value of House in 7 years = $168,302.25
Now, let's calculate the equity in the house. Equity represents the portion of the house that you own outright and is calculated by subtracting the outstanding mortgage balance from the value of the house.
To calculate the outstanding mortgage balance after seven years, we can use an amortization schedule. However, since the mortgage term is 15 years, we need to determine the remaining number of months after seven years:
Remaining Months = Total Mortgage Term - Number of Years
Remaining Months = 180 months - 84 months (7 years)
Remaining Months = 96 months
Using the remaining months and the provided interest rate (6 percent), we can calculate the outstanding mortgage balance using a mortgage calculator or formula. Assuming the mortgage is a fixed-rate mortgage, the calculation would include the principal amount, interest rate, and remaining loan term.
The equity in the house is then calculated as:
Equity = Value of House in 7 years - Outstanding Mortgage Balance
As the calculation of the outstanding mortgage balance requires detailed computations, it is recommended to use a mortgage calculator or consult with a financial advisor to obtain an accurate value for the equity in the house.