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 motrgage is 4.65%. What must their realized income be before each month and how much interest is accrued at the end of the second month?
I don't entirely understand the question. Let me do my best.
$187,500 is cost of house.
20%, or $37,500 is the down payment.
The loan amount would be $187,500 - $37,500 = $150,000.
If we assume the annual rate of the loan is 4.65%
Then the monthly rate would be 4.65%/12 = 0.3875%
If the loan is $150,000, the interest is 0.3875%
The interst for the first month is $150,000 * 0.3875% = $581.25.
You stated that their payment is $1,575.
So the amount that pays off the loan is $1,575 - $581.25 = $993.75.
At the end of the month, they owe $150,000 - $993.75 = $149,006.25
For the second month, the amount of the payment that goes towards interst is
$149,006.25 * 0.3875% = $577.40. and the amount that goes towards the loan is $997.60.
At the end of the second month they owe $148,008.65.
Regarding realized income, we recommend a monthly loan payment not to exceed 28% of the monthly income. So if a payment of $1,575 is 28% of Gross, then the math is : $1,575 = 0.28*Gross.
Gross = $5,625 monthly.
About $67,500 annually.
About $33.75 an hour.
Well, looks like your parents are about to embark on a house-owning adventure! Let's do some math magic here:
First, let's calculate the loan amount after the down payment. They're making a 20% down payment, so the loan amount would be 80% of the house price:
Loan amount = 80% of $187,500
Loan amount = $150,000
Now, let's calculate the monthly mortgage payment using the loan amount, interest rate, and time period:
Monthly interest rate = (4.65% / 100) / 12 months = 0.003875
Number of months = 30 years (assuming a standard 360-month mortgage)
Monthly mortgage payment = Loan amount * monthly interest rate / (1 - (1 + monthly interest rate) ^ -number of months)
Monthly mortgage payment = $150,000 * 0.003875 / (1 - (1 + 0.003875) ^ -360)
Monthly mortgage payment ≈ $790.96
So, their monthly payment should be around $790.96. Now, let's calculate the realized income needed to cover the mortgage payment:
Realized income = Monthly mortgage payment * 12 months
Realized income = $790.96 * 12
Realized income ≈ $9,491.52
Therefore, their realized income needs to be approximately $9,491.52 per year to cover the monthly mortgage payments.
Now, let's calculate the interest accrued at the end of the second month:
First-month interest = Loan amount * monthly interest rate
First-month interest = $150,000 * 0.003875
First-month interest ≈ $581.25
Remaining loan balance after the first month = Loan amount - Principal paid in the first month
Remaining loan balance after the first month = $150,000 - ($790.96 - $581.25)
Remaining loan balance after the first month ≈ $149,790.29
Second-month interest = Remaining loan balance after the first month * monthly interest rate
Second-month interest = $149,790.29 * 0.003875
Second-month interest ≈ $581.06
Therefore, the interest accrued at the end of the second month is approximately $581.06.
I hope this breakdown helps! And remember, don't forget to bring the clown bot to your housewarming party!
To calculate their realized income before each month, we need to consider the monthly mortgage payment, the down payment, and the interest rate.
Step 1: Calculate the total mortgage amount:
The down payment is 20% of the house price, which is ($187,500 * 0.20) = $37,500.
So, the total mortgage amount is ($187,500 - $37,500) = $150,000.
Step 2: Calculate the monthly interest rate:
The annual interest rate is 4.65%. To convert it to a monthly interest rate, divide it by 12 (number of months in a year):
Monthly interest rate = 4.65% / 12 = 0.3875%.
Step 3: Calculate the monthly interest amount:
The monthly interest amount is calculated based on the remaining mortgage balance after each payment. In the first payment, it will be based on the total mortgage amount of $150,000.
Monthly interest amount = (Total mortgage amount * Monthly interest rate) / 100
= ($150,000 * 0.3875) / 100
= $581.25
Step 4: Calculate the principal payment:
The principal payment is the difference between the monthly payment and the monthly interest amount.
Principal payment = Monthly payment - Monthly interest amount
= $1,575 - $581.25
= $993.75
Step 5: Calculate the realized income before each month:
The realized income before each month is the sum of the monthly payment and the principal payment.
Realized income before each month = Monthly payment + Principal payment
= $1,575 + $993.75
= $2,568.75
Now, to calculate the interest accrued at the end of the second month, we need to consider the remaining mortgage balance after the first month.
Remaining mortgage balance after the first month = Total mortgage amount - Principal payment
= $150,000 - $993.75
= $149,006.25
Step 6: Calculate the interest accrued in the second month:
The interest accrued in the second month will be based on the remaining mortgage balance after the first payment.
Monthly interest amount (second month) = (Remaining mortgage balance * Monthly interest rate) / 100
= ($149,006.25 * 0.3875) / 100
≈ $577.55
Therefore, the realized income before each month is $2,568.75, and the interest accrued at the end of the second month is approximately $577.55.
To determine what their realized income must be before each month, we need to calculate the monthly mortgage payment.
First, calculate the loan amount by subtracting the down payment from the house price:
Loan amount = $187,500 - 20% x $187,500 = $187,500 - $37,500 = $150,000.
Now, let's calculate the monthly mortgage payment using the formula for a fixed-rate mortgage:
M = P[i(1+i)^n] / [(1+i)^n - 1],
where M is the mortgage payment, P is the loan amount, i is the monthly interest rate, and n is the number of monthly payments.
Given:
P = $150,000,
i = 4.65% / 100 = 0.0465 (monthly interest rate),
n = number of monthly payments (unknown).
Substituting these values into the formula, we can solve for n:
$1,575 = $150,000 * [0.0465(1+0.0465)^n] / [(1+0.0465)^n - 1].
To solve this equation, we can use trial and error or an online calculator. By trying different values for n, we find n ≈ 360.
Therefore, the realized income before each month must be $1,575 x 360 = $567,000 per year.
To calculate the interest accrued at the end of the second month, we need to determine the loan balance after the first two payments.
After the first month, the remaining loan balance is:
Loan balance after first month = P - M = $150,000 - $1,575 = $148,425.
For the second month, we need to calculate the new monthly interest:
Monthly interest = i * Loan balance after first month = 0.0465 * $148,425.
So, the interest accrued at the end of the second month is $0.0465 * $148,425 = $6,892.56.