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? (6 points: 2 points for correct answer, 4 points for showing work)
To find out the amount of their realized income before each month, we need to calculate the monthly mortgage payment.
Let's start by determining the loan amount. They are making a 20% down payment, so the loan amount is the remaining 80% of the house price:
Loan Amount = House Price - Down Payment
Loan Amount = $180,000 - (20% * $180,000)
Loan Amount = $180,000 - $36,000
Loan Amount = $144,000
Next, we can calculate the monthly mortgage payment using the loan amount and the interest rate. We can use the formula for the monthly payment of a fixed-rate mortgage:
Monthly Payment = (Loan Amount * Monthly Interest Rate) / (1 - (1 + Monthly Interest Rate)^(-Number of Months))
Now let's plug in the values. The interest rate is 4%, which needs to be converted to a monthly interest rate by dividing it by 12 (assuming it's an annual rate):
Monthly Interest Rate = 4% / 12
Monthly Interest Rate = 0.04 / 12
Monthly Interest Rate = 0.00333 (rounded to 5 decimal places)
Number of Months = 30 years * 12 months/year = 360 months
Monthly Payment = ($144,000 * 0.00333) / (1 - (1 + 0.00333)^(-360))
After calculating this, we find that the monthly mortgage payment is approximately $684.03.
To determine the realized income before each month, we add the monthly mortgage payment to the expected payment amount:
Realized Income = Monthly Mortgage Payment + Expected Payment
Realized Income = $684.03 + $1,500
Realized Income = $2,184.03
Therefore, their realized income before each month should be approximately $2,184.03.
To calculate the interest accrued at the end of the second month, we need to know the outstanding loan balance after the first month. To find that, we subtract the principal paid in the first month from the initial loan amount.
Principal Paid = Monthly Mortgage Payment - (Loan Amount * Monthly Interest Rate)
Principal Paid = $684.03 - ($144,000 * 0.00333)
After calculating this, we find that the principal paid in the first month is approximately $214.69.
Outstanding Loan Balance after First Month = Loan Amount - Principal Paid
Outstanding Loan Balance after First Month = $144,000 - $214.69
After calculating this, we find that the outstanding loan balance after the first month is approximately $143,785.31.
To calculate the interest accrued at the end of the second month, we need to calculate the interest for the second month on the outstanding loan balance.
Interest Accrued at the End of the Second Month = Outstanding Loan Balance after First Month * Monthly Interest Rate
Interest Accrued at the End of the Second Month = $143,785.31 * 0.00333
After calculating this, we find that the interest accrued at the end of the second month is approximately $477.15.
To calculate the realized income before each month, we need to subtract the down payment from the total cost of the house.
The down payment is 20% of $180,000, which is 0.20 * $180,000 = $36,000.
So, their realized income before each month is $180,000 - $36,000 = $144,000.
Next, we need to calculate the monthly mortgage payment.
The loan amount is the total cost of the house minus the down payment, which is $180,000 - $36,000 = $144,000.
The interest rate is 4%, which is 0.04 as a decimal.
The loan term is the number of months they will be making payments.
Now, we can calculate the monthly payment using the formula for a fixed-rate mortgage:
Monthly payment = [ loan amount * (interest rate / 12) ] / (1 - (1 + interest rate / 12) ^ (-loan term) )
In this case, the interest rate is 4%, which is 0.04 as a decimal.
Assuming the loan term is 30 years, or 360 months, we can calculate the monthly payment.
Monthly payment = [ $144,000 * (0.04 / 12) ] / (1 - (1 + 0.04 / 12) ^ (-360) )
Using a calculator, we find that the monthly mortgage payment is approximately $687.63 (rounded to the nearest cent).
To find how much interest is accrued at the end of the second month, we need to calculate the interest paid for the first two months.
The interest paid for the first month can be calculated by multiplying the loan amount by the monthly interest rate:
Interest paid for the first month = $144,000 * (0.04 / 12) = $480.
For the second month, the interest paid will be based on the remaining balance after the first payment.
The remaining balance after the first payment can be calculated by subtracting the principal portion of the first payment from the loan amount:
Remaining balance after first payment = $144,000 - ($687.63 - $480) = $143,792.37.
The interest paid for the second month can be calculated by multiplying the remaining balance by the monthly interest rate:
Interest paid for the second month = $143,792.37 * (0.04 / 12) = $479.31 (rounded to the nearest cent).
Therefore, the interest accrued at the end of the second month is approximately $479.31.