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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?
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To find out the realized income before each month, we first need to calculate the amount of the mortgage.
The down payment is 20% of $187,500:
0.20 * $187,500 = $37,500
So the mortgage amount is the total price minus the down payment:
$187,500 - $37,500 = $150,000
Next, we need to calculate the monthly payment. To determine the monthly payment, we will use the formula for calculating the monthly payment on a mortgage:
M = P [ r*(1 + r)^n ] / [ (1 + r)^n - 1]
Where:
M = monthly payment
P = principal amount (the loan amount)
r = monthly interest rate (annual interest rate divided by 12 months)
n = number of months
Plugging in the values, we get:
M = $150,000 [ 0.0465*(1 + 0.0465)^360 ] / [ (1 + 0.0465)^360 - 1]
M = $150,000 [ 0.0465*(1.0465)^360 ] / [ (1.0465)^360 - 1]
M = $150,000 [0.0465*5.0843] / [5.0843 - 1]
M = $150,000 [0.2364255] / 4.0843
M = $35,463.82
So, each month, the payment is $35,463.82. To get the realized income before each month, we add this monthly payment to the down payment:
$35,463.82 + $37,500 = $72,963.82
Therefore, your parents' realized income before each month must be $72,963.82.
are you sure
I apologize for the error. Let me correct my calculations:
After calculating the mortgage amount, we need to calculate the monthly payment using the formula for a fixed-rate mortgage, which is:
M = P[r(1 + r)^n] / [(1 + r)^n - 1]
Where:
M = monthly payment
P = principal amount (the loan amount)
r = monthly interest rate (annual interest rate divided by 12 months)
n = number of months
Plugging in the values, we get the monthly payment as follows:
M = $150,000 [0.0465*(1 + 0.0465)^360] / [(1 + 0.0465)^360 - 1]
M = $150,000 [0.0465*1.0465^360] / [1.0465^360 - 1]
M = $150,000 [0.0465*11.7871] / [11.7871 - 1]
M = $150,000 [0.5481] / 10.7871
M = $150,000 * 0.0508 / 10.7871
M = $712.80
The monthly payment is $712.80.
To find the realized income before each month, we add the monthly payment to the down payment:
$712.80 + $37,500 = $38,212.80
Therefore, your parents' realized income before each month must be $38,212.80.