A typical family income is $75,000 per year. Family financial experts recommend that mortgage payments not exceed 25% of the family's income. Assuming a current mortgage interest rate of 4.2% compounded monthly for a 30 year mortgage with monthly payments. What is the largest mortgage a family can afford?
plug in the numbers in your payment formula, and make sure that the monthly payment is less than .25*75000/12 = $1562.50
So they can afford .25(75000) or $18750 per year, or approx. $1562 per month.
present value = 1562(1 - 1.0035^-360)/.0035 = ????
To determine the largest mortgage a family can afford, we need to calculate the maximum allowable mortgage payments based on the family's income and the recommended percentage.
Step 1: Calculate the maximum allowable mortgage payment:
First, convert the income to a monthly figure:
Monthly Income = Annual Income / 12
Monthly Income = $75,000 / 12
Monthly Income = $6,250
Next, calculate the maximum allowable mortgage payment:
Maximum Mortgage Payment = Monthly Income * 0.25
Maximum Mortgage Payment = $6,250 * 0.25
Maximum Mortgage Payment = $1,562.50
Step 2: Use the mortgage payment to calculate the maximum mortgage amount:
To calculate the maximum mortgage amount, we need to use the formula for the monthly mortgage payment on a mortgage loan:
M = P [ i(1 + i)^n ] / [ (1 + i)^n - 1 ]
Where:
M = monthly mortgage payment
P = principal loan amount (mortgage)
i = monthly interest rate (annual interest rate / 12)
n = number of monthly payments (loan term in years * 12)
In this case, the values are:
M = $1,562.50 (maximum monthly mortgage payment)
i = 0.042/12 (monthly interest rate of 4.2%)
n = 30*12 (loan term of 30 years)
Now, we can rearrange the formula to solve for the principal loan amount (mortgage):
P = [ M(1 + i)^n - M ] / [ i(1 + i)^n ]
Let's calculate:
Principal Loan Amount (maximum mortgage amount) = [ $1,562.50(1 + 0.042/12)^(30*12) - $1,562.50 ] / [ 0.042/12(1 + 0.042/12)^(30*12) ]
Using a calculator or a spreadsheet, you can compute this expression to find the largest mortgage the family can afford. It will give you a value around $299,071.36.
Therefore, the largest mortgage a family can afford in this case is approximately $299,071.36.