You can afford monthly payments of $1200. If current mortgage rates are 7.5% for a 30-year fixed rate loan, what loan principal can you afford? If you are required to make a 20% down payment and you have cash on hand to do it, what price home can you afford?
To determine the loan principal you can afford, we need to calculate the maximum amount you can borrow based on your monthly payments and the mortgage rate.
Step 1: Convert the annual interest rate to a monthly interest rate. Divide the annual interest rate by 12 to get the monthly rate.
Monthly interest rate = Annual interest rate / 12
Monthly interest rate = 7.5% / 12 = 0.625% or 0.00625 in decimal form.
Step 2: Use the loan affordability formula to calculate the loan principal you can afford. The formula is:
Loan principal = (Monthly payment) / (Monthly interest rate * (1 + Monthly interest rate)^(Number of months))
In this case, the monthly payment is $1200, the monthly interest rate is 0.00625, and the loan duration is 30 years (or 360 months).
Loan principal = $1200 / (0.00625 * (1 + 0.00625)^360)
Calculation:
Loan principal = $1200 / (0.00625 * 1.00625^360) = $154,051.82 (rounded to the nearest dollar)
Therefore, with a monthly payment of $1200 and a mortgage rate of 7.5% for a 30-year fixed rate loan, you can afford a loan principal of approximately $154,051.82.
Now, let's calculate the price of the home you can afford with a 20% down payment.
Step 1: Determine the down payment amount.
The down payment is 20% of the home price. Multiply the loan principal by 0.2 to get the down payment amount.
Down payment = Loan principal * 0.2
Down payment = $154,051.82 * 0.2 = $30,810.36
Step 2: Calculate the maximum affordable home price.
The maximum affordable home price can be calculated by adding the down payment to the loan principal.
Maximum affordable home price = Loan principal + Down payment
Maximum affordable home price = $154,051.82 + $30,810.36 = $184,862.18 (rounded to the nearest dollar)
Therefore, with a 20% down payment, you can afford a home price of approximately $184,862.18.