The price of a home is $120,000. The bank requires a 10%

down payment and two points of closing. The cost of the home
is financed with 30-year fixed-rate mortgage at 8.5%.
Find the total cost of interest over 30 years.

To find the total cost of interest over 30 years, we need to calculate the mortgage amount, the monthly payment, and the total interest paid.

1. Calculate the down payment:
The down payment is 10% of the home price, which is $120,000 * 0.10 = $12,000.

2. Calculate the closing cost:
Two points on the closing cost is calculated by multiplying the loan amount by 0.02.
Loan amount = Home price - Down payment = $120,000 - $12,000 = $108,000.
Closing cost = $108,000 * 0.02 = $2,160.

3. Calculate the loan amount:
Loan amount = Home price - Down payment + Closing cost = $120,000 - $12,000 + $2,160 = $110,160.

4. Calculate the monthly interest rate:
Monthly interest rate = Annual interest rate / 12 = 0.085 / 12 = 0.0070833.

5. Calculate the number of monthly payments over 30 years:
Number of monthly payments = Number of years * 12 = 30 * 12 = 360.

6. Calculate the monthly payment using the formula for a fixed-rate mortgage:
Monthly payment = Loan amount * (monthly interest rate * (1 + monthly interest rate)^number of payments) / ((1 + monthly interest rate)^number of payments - 1)
Monthly payment = $110,160 * (0.0070833 * (1 + 0.0070833)^360) / ((1 + 0.0070833)^360 - 1).
Monthly payment ≈ $808.96.

7. Calculate the total interest paid over 30 years:
Total interest paid = Monthly payment * Number of payments - Loan amount.
Total interest paid = $808.96 * 360 - $110,160.
Total interest paid ≈ $190,827.60.

Therefore, the total cost of interest over 30 years is approximately $190,827.60.

To find the total cost of interest over 30 years, we first need to calculate the mortgage loan amount and the monthly mortgage payment. Then, we can calculate the total interest paid over the 30-year period.

Step 1: Calculate the mortgage loan amount
The down payment required by the bank is 10% of the home price. So, the down payment can be calculated as follows:
Down payment = 10% of $120,000 = 10/100 * $120,000 = $12,000

The closing cost is given as two points of the loan amount. One point is equal to 1% of the loan amount. Therefore, the closing cost can be calculated as follows:
Closing cost = 2 points * Mortgage loan amount
Since the loan amount is not known yet, we will use the closing cost to calculate it later.

To find the mortgage loan amount, subtract the down payment and closing cost from the home price:
Mortgage loan amount = Home price - Down payment - Closing cost

Step 2: Calculate the monthly mortgage payment
To calculate the monthly mortgage payment, we can use the loan amount, interest rate, and loan term in the following formula:
M = (P * r * (1 + r)^n) / ((1 + r)^n - 1)
where M is the monthly mortgage payment, P is the loan amount, r is the monthly interest rate, and n is the total number of payments (number of years * 12).

The monthly interest rate can be found by dividing the annual interest rate by 12:
Monthly interest rate = 8.5% / 100 / 12 = 0.085 / 12 = 0.0070833

The total number of payments is the loan term in years multiplied by 12:
Total number of payments = 30 * 12 = 360

Now, we have all the values needed to calculate the monthly mortgage payment.

Step 3: Calculate the total interest paid
The total interest paid over the 30-year period can be calculated by subtracting the loan amount from the total amount paid over the loan term. The total amount paid can be calculated by multiplying the monthly mortgage payment by the total number of payments.

Total interest paid = (Monthly mortgage payment * Total number of payments) - Mortgage loan amount

Let's calculate the values:

Down payment = $12,000
Closing cost = 2 points * Mortgage loan amount
Monthly interest rate = 0.0070833
Total number of payments = 360

To calculate the mortgage loan amount:
Mortgage loan amount = $120,000 - $12,000 - Closing cost

To calculate the monthly mortgage payment:
Monthly mortgage payment = (Mortgage loan amount * Monthly interest rate * (1 + Monthly interest rate)^Total number of payments) / ((1 + Monthly interest rate)^Total number of payments - 1)

Finally, to calculate the total interest paid:
Total interest paid = (Monthly mortgage payment * Total number of payments) - Mortgage loan amount

The amount of the loan is $120,000 -10% + 2% = $110,400, assuming the "points" are added to the financed amount.

Using the amortization table at
http://www.fenclwebdesign.com/amortization-calculator.htm
I find that the monthly payment will be
$848.89. There will be 360 such payments over 30 years, for a total payment amount of $305,600. Subract the original principle (110,400) from that to get the interest paid.

The amount of the loan is $120,000 -10% + 2% = $110,400, assuming the "points" are added to the financed amount.

R = Pi/[1 - (1+i)^(-n)] where
P = 110,400
R = the monthly payment
i = 8.5/[100(12)] = .007083...
n = 30(12) = 360 yielding
R = $848.88 per month.

Therefore, the total interest paid is 360(848.88) - 100,400.