You can afford 800 a month  You found a 30 year loan at 6.7 interest  How big of a loan can you afdord how much total money will you pay the company and how much is interest

To determine how big of a loan you can afford, we can use the following formula for a fixed-rate mortgage:

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

Where:
- $M$ is the monthly mortgage payment ($800 in this case),
- $P$ is the principal (the loan amount we are trying to find),
- $r$ is the monthly interest rate (annual rate divided by 12),
- $n$ is the number of payments (loan term in months).

### Step 1: Calculate the monthly interest rate.
Given the annual interest rate of 6.7%, we convert it to a monthly rate:
\[
r = \frac{6.7\%}{12} = 0.005583 \text{ (or 0.005583 in decimal form)}
\]

### Step 2: Calculate the number of payments.
For a 30-year loan, the number of monthly payments is:
\[
n = 30 \times 12 = 360 \text{ payments}
\]

### Step 3: Solve for the loan amount $P$.
We now rearrange the formula to solve for $P$:

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

Substituting the known values $M = 800$, $r = 0.005583$, and $n = 360$, we can calculate the loan amount $P$.

Let's compute this.The loan amount you can afford with a monthly payment of $800 is approximately **$123,978**.

### Step 4: Calculate the total amount paid over the life of the loan.
To find the total amount you'll pay, multiply your monthly payment by the number of payments:

\[
\text{Total Payment} = M \times n
\]

Let's calculate that next.The total amount you will pay over the 30-year period is **$288,000**.

### Step 5: Calculate the total interest paid.
To find how much of this total is interest, subtract the original loan amount from the total payment:

\[
\text{Total Interest} = \text{Total Payment} - P
\]

Let's compute the total interest.The total interest you will pay over the life of the loan is approximately **$164,022**.

### Summary:
- **Loan Amount (Principal):** $123,978
- **Total Payment (Over 30 years):** $288,000
- **Total Interest Paid:** $164,022

Would you like any more details or have further questions?

Here are some related questions you might consider:
1. How does the loan amount change with a higher or lower interest rate?
2. What if the loan term is reduced to 15 years instead of 30 years?
3. How does making extra payments affect the total interest paid?
4. How much will you save by getting a 6.0% interest rate instead of 6.7%?
5. What is the benefit of refinancing after a few years?

**Tip:** Making small extra payments toward your loan principal can significantly reduce the amount of interest paid over time.

You can afford 800 a month. You found a 30-year loan at 6.7% interest. How big of a loan can you afford? How much total money will you pay the company, and how much is interest?

Learn how to calculate the maximum loan amount you can afford with a 30-year mortgage at 6.7% interest and a monthly payment of $800. This detailed guide covers financial math concepts like loan amortization and interest calculation. Find out the total payment and interest you will pay over the life of the loan.

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