Your parents are buying a house for $180,000. They have a good credit rating, are
making a 20% down payment, and expect to pay $1,500/month. The interest rate for the motrgage is
4%. What must their realized income be before each month and how much interest is accrued at the
end of the second month?
will finance 4/5 of the cost: 144000
First month interest: .04(144000)/12=480
1500-480=1020=principal paid first month
New principal: 144000-1020=142980
Second month interest: .04(142980)/12=476.60
First two months accrued interest: 480+476.60=956.60
I guess their realized income must be enough to make the payment. There may be rules for this that I don't know about. But at a minimum it has to be $1500 plus living expenses.
thank you
To calculate the monthly mortgage payment, we need to use the formula:
M = P [ i(1 + i)^n ] / [ (1 + i)^n – 1 ]
Where:
M = Monthly payment
P = Loan amount (in this case, $180,000 - 20% down payment = $144,000)
i = Monthly interest rate (4% divided by 12 months = 0.00333)
n = Number of payments (2 months in this case)
Let's calculate the monthly mortgage payment first:
M = $144,000 [ 0.00333(1 + 0.00333)^2 ] / [ (1 + 0.00333)^2 – 1 ]
M = $144,000 [ 0.00333(1.00333)^2 ] / [ (1.00333)^2 – 1 ]
M = $144,000 [ 0.00333(1.006671) ] / [ (1.006671) – 1 ]
M = $144,000 [ 0.0005347 ] / [ 0.00667 ]
M = $144,000 [ 0.080221 ]
M = $11,557.56
Therefore, their monthly mortgage payment is $11,557.56.
To calculate their realized income before each month, we need to add the mortgage payment to their monthly expenses.
Realized income before each month = Monthly mortgage payment + Monthly expenses
Their monthly expenses are $1,500.
Realized income before each month = $11,557.56 + $1,500
Realized income before each month = $13,057.56
The interest accrued at the end of the second month can be calculated by multiplying the loan balance at the end of the first month by the monthly interest rate.
Loan balance at the end of the first month = Loan amount - (Monthly payment - Interest)
Loan amount = $144,000
Monthly payment = $11,557.56
Interest = Loan amount * Monthly interest rate
Interest = $144,000 * 0.00333
Interest = $478.32
Loan balance at the end of the first month = $144,000 - ($11,557.56 - $478.32)
Loan balance at the end of the first month = $132,920.76
Interest accrued at the end of the second month = Loan balance at the end of the first month * Monthly interest rate
Interest accrued at the end of the second month = $132,920.76 * 0.00333
Interest accrued at the end of the second month = $442.16
Therefore, the interest accrued at the end of the second month is $442.16.