Question
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?
Answers
GPT 3.5
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.
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.