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.