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"You buy a home for $177,831 and put $11,459 down. You borrow the remainder. The mortgage company also charges a 3% loan and closing fee, which you must also borrow. The interest rate is 6.5% for 30 years. Calculate the total cost of credit assuming you make the monthly payments for the full number of years."

Let's break this down:

### Step 1: Determine the amount borrowed.
- Home price: $177,831
- Down payment: $11,459
- Remaining amount to borrow:  
  \[
  \text{Remaining amount} = 177,831 - 11,459 = 166,372
  \]

### Step 2: Add the 3% loan and closing fee.
You are also borrowing an additional 3% fee on this amount:
\[
\text{3% Fee} = 166,372 \times 0.03 = 4,991.16
\]
So, the total loan amount becomes:
\[
\text{Total Loan} = 166,372 + 4,991.16 = 171,363.16
\]

### Step 3: Use the mortgage formula to calculate the monthly payment.
The formula for monthly mortgage payments is:
\[
M = P \times \frac{r(1+r)^n}{(1+r)^n - 1}
\]
Where:
- $M$ is the monthly payment,
- $P$ is the loan amount (\$171,363.16),
- $r$ is the monthly interest rate (annual rate / 12) = $0.065 / 12 = 0.0054167$,
- $n$ is the total number of payments (30 years $\times$ 12 months/year = 360 months).

Substituting these values into the formula:

\[
M = 171,363.16 \times \frac{0.0054167(1+0.0054167)^{360}}{(1+0.0054167)^{360} - 1}
\]

Calculating the above gives the monthly payment $M$.

### Step 4: Calculate the total cost of credit.
The total cost of credit over the 30 years would be the monthly payment multiplied by the total number of months:
\[
\text{Total Cost} = M \times 360
\]

Let me now compute the exact values for you.The monthly mortgage payment would be approximately **$1,083.13**.

The total cost of credit over 30 years, assuming all payments are made, is about **$389,927.43**.

### Answer choices:
- The total cost is closest to **$256,898.14**, which is incorrect because the actual total cost is much higher.

Would you like more details or have any questions?

### Related Questions:
1. How does the total interest paid compare to the loan amount?
2. What happens if the interest rate decreases by 1%?
3. How does a 15-year mortgage change the total cost of credit?
4. What if the 3% closing fee is paid upfront instead of added to the loan?
5. How would bi-weekly payments affect the overall cost?

### Tip:
When calculating total loan costs, always include any additional fees or charges added to the loan amount, as they significantly affect the total interest paid over time.

You buy a home for $177,831 and put $11,459 down. You borrow the remainder. The mortgage company also charges a 3% loan and closing fee which you must also borrow. The interest rate is 6.5% for 30 years. Calculate the total cost of credit assuming you make the monthly payments for the full number of years.

This problem walks through the steps of calculating the total cost of a mortgage loan for a home priced at $177,831 with a down payment of $11,459, including a 3% loan fee. It uses the standard mortgage formula and a 6.5% interest rate over 30 years.

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