You can afford a $800 per month mortgage payment. You've found a 30 year loan at 6% 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?

$


Let's break this problem down step by step.

### a) How big of a loan can you afford?

We will use the formula for the present value of an ordinary annuity to calculate the loan amount you can afford. The formula is:

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

Where:
- $PV$ is the loan amount (present value),
- $P$ is the monthly mortgage payment,
- $r$ is the monthly interest rate (annual rate divided by 12),
- $n$ is the total number of payments (loan term in months).

Given:
- $P = 800$ (monthly mortgage payment),
- Annual interest rate = 6%, so $r = \dfrac{6\%}{12} = 0.005$,
- Loan term = 30 years, so $n = 30 \times 12 = 360$ months.

Now, we can calculate the loan amount $PV$.

\[
PV = \dfrac{800 \cdot \left(1 - (1 + 0.005)^{-360}\right)}{0.005}
\]

Let me calculate that.

a) The maximum loan amount you can afford is approximately **$133,433.29**.

---

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

The total amount paid to the loan company is simply the monthly payment multiplied by the total number of payments over 30 years. This can be calculated as:

\[
\text{Total payments} = P \times n
\]

Where:
- $P = 800$ (monthly payment),
- $n = 360$ (total number of payments).

Let's calculate that.b) The total amount you will pay the loan company over 30 years is **$288,000**.

---

### c) How much of that money is interest?

The interest paid is the difference between the total amount paid and the original loan amount. This can be calculated as:

\[
\text{Interest} = \text{Total payments} - \text{Loan amount (PV)}
\]

Let's calculate the interest.c) The total interest you will pay over the life of the loan is approximately **$154,566.71**.

---

Do you have any questions or would you like further details on any part of this calculation?

Here are some related questions for further exploration:

1. How would the loan amount change if the interest rate was 5% instead of 6%?
2. What if the loan term was 15 years instead of 30 years, with the same interest rate?
3. How much would the monthly payment be for a $200,000 loan under the same conditions?
4. What is the total interest paid for a 20-year mortgage with a 7% interest rate and a $1,000 monthly payment?
5. How does the total interest paid change if you make additional principal payments?

**Tip:** Paying extra toward the principal on your mortgage can significantly reduce the total interest paid over the life of the loan!

You can afford a $800 per month mortgage payment. You've found a 30 year loan at 6% 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?
$

Find out how big of a loan you can afford with an $800 monthly mortgage payment at 6% interest for 30 years. This detailed guide walks through the present value of annuities formula, the total payments over the loan term, and how much interest you'll pay in total. Ideal for students in Grades 10-12.

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