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?

Be sure to include the following in your response:
the answer to the original question
the mathematical steps for solving the problem demonstrating mathematical reasoning

Answer 1

To determine the required realized income for your parents, we need to use the formula for calculating mortgage payments:

P = (PV * r * (1 + r)^n) / ((1 + r)^n - 1)

where P is the monthly payment, PV is the mortgage principal ($187,500 - 20% down payment = $150,000), r is the monthly interest rate (4.65% / 12 = 0.3875%), and n is the number of months (30 years or 360 months).

Substituting the given values, we get:

P = ($150,000 * 0.003875 * (1 + 0.003875)^360) / ((1 + 0.003875)^360 - 1)

P = $802.62

Therefore, your parents must have a realized income of $1,575 + $802.62 = $2,377.62 before each month to afford the mortgage payment.

Note: This calculation assumes that the monthly payment of $1,575 includes both the principal and interest payments for the mortgage.