Your parents are buying a house for $187,500. They have a good credit rating, are making a 20% down payment, and expect to pay $1,575/month. The interest rate for the mortgage is 4.65%. What must their realized income be before each month?
In order to calculate their realized income before each month, we can use the formula for the monthly mortgage payment:
M = P [ r(1 + r)^n ] / [ (1 + r)^n - 1]
where:
M = monthly mortgage payment
P = principal amount of the loan ($187,500 - 20% down payment = $150,000)
r = monthly interest rate (4.65%/12 = 0.003875)
n = total number of payments (30 years = 360 months)
Plugging in the values, we get:
M = 150,000 [ 0.003875(1 + 0.003875)^360 ] / [ (1 + 0.003875)^360 - 1]
M = 150,000 [ 0.003875(1.003875)^360 ] / [ (1.003875)^360 - 1]
M = 150,000 [ 0.745480 ] / [ 2.70328 - 1]
M = 150,000 [ 0.745480 ] / [ 1.70328]
M = 65,62.57
Their realized income before each month must be at least $6,562.57.