Freddie Sue has a monthly gross income of $2950 and total monthly debt payments of $160. She will have to make a down payment of 15% of the purchase price of a new home and estimates that the monthly property tax and insurance cost will be $210. If she can get a 30 year loan at 8% how much home can she afford?
To determine how much home Freddie Sue can afford, we need to consider her monthly income, debt payments, down payment, monthly property tax and insurance cost, and the terms of the loan.
1. Calculate Freddie Sue's annual gross income: $2950 x 12 = $35,400.
2. Determine Freddie Sue's maximum monthly debt-to-income ratio. Most lenders use a maximum ratio of 43%, which means your total monthly debt payments (including the mortgage) should not exceed 43% of your monthly gross income.
Maximum monthly debt payments = $35,400 * 0.43 = $15,222.
3. Subtract Freddie Sue's current monthly debt payments from the maximum to find out how much she can allocate to her mortgage payment:
Maximum mortgage payment = $15,222 - $160 = $15,062.
4. Calculate the maximum amount Freddie Sue can borrow by determining the monthly mortgage payment based on the loan terms.
a. Convert the annual interest rate to a monthly rate: 8% / 100 / 12 = 0.00667.
b. Determine the number of monthly payments over 30 years: 30 years * 12 months = 360 months.
c. Calculate the monthly mortgage payment using the formula:
M = P [ i(1 + i)^n ] / [ (1 + i)^n - 1 ]
Where M is the monthly payment, P is the loan amount, i is the monthly interest rate, and n is the total number of payments.
Let's calculate the maximum loan amount:
Loan amount = M * [ (1 + i)^n - 1 ] / (i * (1 + i)^n)
We know that Freddie Sue's maximum mortgage payment is $15,062 and i is 0.00667. Using the formula:
Loan amount = $15,062 * [ (1 + 0.00667)^360 - 1 ] / (0.00667 * (1 + 0.00667)^360).
This calculation will yield the maximum loan amount Freddie Sue can afford.
5. Deduct Freddie Sue's down payment from the maximum loan amount to determine the maximum purchase price for her new home.
Purchase price = Maximum loan amount - (15% of purchase price).
Rearrange the formula to solve for the purchase price:
Purchase price + 0.15 * purchase price = Maximum loan amount.
Simplify the equation:
1.15 * purchase price = Maximum loan amount.
Finally, divide both sides by 1.15 to solve for the purchase price:
Purchase price = Maximum loan amount / 1.15.
By following these steps, you can calculate how much home Freddie Sue can afford, given her income, debts, down payment, and loan terms.