If a home buyer purchases a home in 2006 for $225,000 with a 10% down payment using a 30 year fixed mortgage rate at 6.5% and 3.5% closing costs added to the original mortgage, compute the following:
a) the original amount of the mortgage loan
b) the home's market value in 7 years if annual appreciation rates are 6%
c) the homeowners equity in the home after 7 years
I am not familiar with US mortgage laws.
What is this "3.5% closing cost" ?
so is the original mortgage:
add 3.5% to 225,000, then take 90% of that?
That would be 225,000(1.035)(.9)
= $209,587.50
confirm that before I proceed
To compute the answers to the questions, we'll go step by step.
a) The original amount of the mortgage loan:
To find the original amount of the mortgage loan, we need to calculate 90% of the purchase price, as the buyer made a 10% down payment.
$225,000 * 0.90 = $202,500
Therefore, the original amount of the mortgage loan is $202,500.
b) The home's market value in 7 years if annual appreciation rates are 6%:
To calculate the home's market value after 7 years with an annual appreciation rate of 6%, we can use the compound interest formula:
A = P(1 + r/n)^(nt)
Where:
A is the future value (market value) of the home
P is the present value (purchase price) of the home
r is the annual interest rate (appreciation rate) divided by 100
n is the number of times the interest is compounded in a year
t is the number of years
Let's calculate it:
P = $225,000
r = 6% divided by 100 = 0.06
n = 1 (since it is compounded annually)
t = 7 years
A = $225,000 * (1 + 0.06/1)^(1*7)
A = $225,000 * (1.06)^7
A = $225,000 * 1.44158733608
Therefore, the home's market value in 7 years would be approximately $324,107.
c) The homeowner's equity in the home after 7 years:
To calculate the homeowner's equity in the home after 7 years, we need to subtract the remaining mortgage loan amount from the current market value of the home.
Remaining mortgage loan amount = Original mortgage loan amount - Principal already paid off
We know the original mortgage loan amount is $202,500. However, we need to calculate the principal already paid off after 7 years. To do this, we can use an amortization calculator or formula.
The formula to calculate the monthly payment (PMT) of a fixed-rate mortgage is as follows:
PMT = P * r * (1 + r)^n / ((1 + r)^n - 1)
Where:
PMT is the monthly payment
P is the principal amount (original mortgage loan amount)
r is the monthly interest rate (annual interest rate divided by 12)
n is the total number of monthly payments (30 years multiplied by 12 months per year)
To find the principal already paid off after 7 years, we need to calculate the total number of monthly payments made in 7 years.
n = 7 years * 12 months per year = 84 total monthly payments
Using the above values, we can solve for PMT (monthly payment) using the original mortgage loan amount ($202,500). We can then calculate the principal already paid off using the number of payments made.
Finally, we can calculate the homeowner's equity:
Homeowner's equity = Market value - Remaining mortgage loan amount
With the market value being approximately $324,107 and the remaining mortgage loan amount calculated above, you can subtract the remaining mortgage loan amount from the market value to find the homeowner's equity after 7 years.