A house is being purchased for $138,000.00. The 30-year mortgage has a 10% down payment, an interest rate of 4.875%, and a PMI payment of $25.88 each month for 77 months. The yearly taxes are $2400.00, and the insurance is $750.00 per year, which is to be placed into an escrow account.
What is the total cost of the loan? Round your answer to the nearest .

To calculate the total cost of the loan, we'll need to consider the following:

1. **Initial House Price**: $138,000.00
2. **Down Payment**: 10% of the house price
3. **Loan Amount**: The amount financed after the down payment
4. **Monthly Mortgage Payment**: This includes the principal and interest on the loan.
5. **Private Mortgage Insurance (PMI)**: Monthly payment of $25.88 for 77 months
6. **Property Taxes**: $2,400 per year
7. **Homeowners Insurance**: $750 per year
8. **Total Interest Paid Over 30 Years**
9. **Escrow Payments**: For taxes and insurance

Let's break down each step.

### 1. Down Payment:
The down payment is 10% of $138,000.

\[
\text{Down Payment} = 0.10 \times 138{,}000 = 13{,}800
\]

### 2. Loan Amount:
The loan amount is the total house price minus the down payment.

\[
\text{Loan Amount} = 138{,}000 - 13{,}800 = 124{,}200
\]

### 3. Monthly Mortgage Payment:
To calculate the monthly mortgage payment, we'll use the following formula for a fixed-rate mortgage:

\[
M = P \frac{r(1+r)^n}{(1+r)^n-1}
\]

where:
- $ M $ is the monthly payment,
- $ P $ is the loan amount ($124,200),
- $ r $ is the monthly interest rate (annual rate divided by 12), and
- $ n $ is the number of payments (30 years $\times$ 12 months = 360).

The annual interest rate is 4.875%, so the monthly interest rate is:

\[
r = \frac{4.875\%}{12} = \frac{0.04875}{12} \approx 0.0040625
\]

Now, substitute the values into the mortgage payment formula:

\[
M = 124{,}200 \times \frac{0.0040625(1+0.0040625)^{360}}{(1+0.0040625)^{360}-1}
\]

Calculating this will give us the monthly mortgage payment.

### 4. PMI Payments:
The PMI is $25.88 per month for 77 months, so the total PMI cost is:

\[
\text{Total PMI} = 25.88 \times 77 = 1{,}992.76
\]

### 5. Escrow Payments:
This includes the yearly taxes and insurance:

\[
\text{Escrow Payments (yearly)} = 2{,}400 + 750 = 3{,}150 \text{ per year}
\]

\[
\text{Escrow Payments (monthly)} = \frac{3{,}150}{12} = 262.50 \text{ per month}
\]

### 6. Total Interest Paid Over 30 Years:
To find the total interest paid, multiply the monthly mortgage payment by 360 (the total number of payments) and subtract the loan principal:

\[
\text{Total Interest} = (M \times 360) - 124{,}200
\]

### 7. Total Cost of the Loan:
Finally, the total cost of the loan includes:
- The down payment
- The total of all monthly mortgage payments over 30 years
- PMI payments
- Total escrow payments (over 30 years)
- Total interest

Let me calculate these step by step.The total cost of the loan is approximately **$346,912.34**.

Would you like a detailed breakdown of these calculations or have any questions?

Here are five related questions you might find useful:
1. How does the interest rate impact the total cost of a loan?
2. What would happen to the monthly mortgage payment if the loan term were shorter?
3. How does a larger down payment affect the overall cost of a mortgage?
4. What is the significance of PMI in a mortgage, and when can it be removed?
5. How would changes in property taxes or insurance premiums affect the total loan cost?

**Tip:** Always compare mortgage offers from different lenders, as even small differences in interest rates can significantly impact the total cost of a loan over 30 years.

Learn how to calculate the total cost of a $138,000 mortgage with a 10% down payment, including interest rates, PMI payments, escrow for taxes and insurance, and total interest over 30 years. Get a detailed breakdown and understand the financial implications. Suitable for advanced learners and anyone interested in mortgage finance.

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