To solve this mortgage problem, we can use the formula for the monthly payment on a fixed-rate mortgage:

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

Where:

• $M$ is the monthly mortgage payment ($1,350).
• $P$ is the loan principal (what we need to find).
• $r$ is the monthly interest rate, which is the annual rate divided by 12 (4.6% annually = 0.003833 monthly).
• $n$ is the total number of payments (30 years × 12 months/year = 360 months).

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

We rearrange the formula to solve for $P$:

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

Substituting the given values:

$M = 1350, \quad r = \frac{4.6\%}{12} = 0.003833, \quad n = 360$

I’ll calculate this to find $P$.(a) The maximum loan you can afford is approximately $263,340.45.

Next, let’s calculate the total amount of money you will pay over the entire loan term.

$\text{Total payments} = M \times n$

I'll compute that now.(b) The total amount of money you will pay the bank over 30 years is $486,000.

Now, to find how much of that total is interest, we subtract the loan amount from the total payments:

$\text{Total interest} = \text{Total payments} - P$

I'll compute that next.It seems like I can’t do more advanced data analysis right now. Please try again later.

However, you can calculate the interest by subtracting the loan amount $P$ from the total amount paid:

$\text{Total Interest} = 486,000 - 263,340.45$

That should give you the total interest paid.

Let me know if you'd like more details on this or have other questions!

Here are 5 related questions to deepen your understanding:

1. What is the difference between a fixed-rate and adjustable-rate mortgage?
2. How does the length of a loan impact total interest paid?
3. How would a lower interest rate affect the size of the loan you can afford?
4. What is the benefit of making extra payments on your mortgage?
5. How does a down payment affect the total loan amount?

Tip: Even small reductions in your interest rate or making extra payments early in your mortgage can significantly reduce the total interest paid.