You can afford a $850 per month mortgage payment. You've found a 30 year loan at 8% interest.

a) How big of a loan can you afford?

$

b) How much total money will you pay the loan company?

$

c) How much of that money is interest?

To solve this problem, we'll use the formula for calculating the monthly mortgage payment on a loan:

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

Where:
- $M$ is the monthly mortgage payment,
- $P$ is the loan amount (which we need to find),
- $r$ is the monthly interest rate,
- $n$ is the total number of payments (months).

Given:
- $M = 850$ (monthly payment),
- The annual interest rate is 8%, so the monthly interest rate $r = \frac{8}{12} \% = 0.00667$,
- The loan is for 30 years, which means $n = 30 \times 12 = 360$ months.

### a) To find the loan amount $P$, we rearrange the formula:

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

Let’s calculate the loan amount $P$.### a) The loan amount you can afford is approximately \$115,841.

### b) To find the total amount of money you will pay over the life of the loan, we multiply the monthly payment by the total number of payments:

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

Let’s calculate that.### b) The total amount of money you will pay the loan company is \$306,000.

### c) To find how much of that is interest, we subtract the loan amount from the total payment:

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

Let's calculate the interest.### c) The total amount of interest you will pay is approximately \$190,159.

Would you like more details or have any questions?

Here are some related questions:
1. What would happen if the interest rate was reduced to 6%?
2. How much would you save in interest if you paid an extra \$100 per month?
3. What is the total interest if the loan term is reduced to 15 years instead of 30 years?
4. How much more could you afford if the interest rate was 7% instead of 8%?
5. What would the monthly payment be for a loan amount of \$150,000 at 8% for 30 years?

**Tip:** Lowering your interest rate even by 1% can significantly reduce the total interest paid over the life of the loan.

You can afford a $850 per month mortgage payment. You've found a 30 year loan at 8% interest.

a) How big of a loan can you afford?

b) How much total money will you pay the loan company?

c) How much of that money is interest?

Learn how to calculate the maximum loan you can afford with an $850 monthly mortgage payment for a 30-year loan at 8% interest. The solution includes step-by-step calculations to determine the loan amount, total payment, and interest paid over the loan's duration.

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