Let's break this down step-by-step:

a) How big of a loan can you afford?

To calculate how much loan you can afford, we will use the monthly mortgage payment formula for a fixed-rate loan:

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

Where:

• $M$ is the monthly mortgage payment
• $P$ is the principal (the loan amount we want to calculate)
• $r$ is the monthly interest rate (annual rate divided by 12)
• $n$ is the total number of payments (loan term in years multiplied by 12)

Given:

• Monthly payment, $M = 950$
• Interest rate, $8\%$ annual, so monthly rate $r = \frac{0.08}{12} = 0.00667$
• Loan term is 30 years, so total payments $n = 30 \times 12 = 360$

Now, rearrange the formula to solve for $P$:

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

Substitute the given values into the formula:

$P = \frac{950 \cdot \left( (1 + 0.00667)^{360} - 1 \right)}{0.00667 \cdot (1 + 0.00667)^{360}}$

Let me calculate that for you. Given values M = 950 # Monthly payment r = 0.08 / 12 # Monthly interest rate (8% annual) n = 30 * 12 # Total number of payments (30 years)

Calculate the loan amount (P)

P = M * (((1 + r) ** n - 1) / (r * (1 + r) ** n)) PThe loan amount you can afford is approximately $129,469.32.

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

To find the total money paid over the course of the loan, we multiply the monthly payment by the number of payments:

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

Substitute the values:

$\text{Total paid} = 950 \times 360$

Let me calculate that for you. Calculate the total money paid over the life of the loan total_paid = M * n total_paidThe total money you will pay to the loan company over 30 years is $342,000.

c) How much of that money is interest?

To find the total interest paid, subtract the principal (loan amount) from the total money paid:

$\text{Total interest} = \text{Total paid} - \text{Principal}$

Substituting the values:

$\text{Total interest} = 342,000 - 129,469.32$

Let me calculate that for you. Calculate the total interest paid total_interest = total_paid - P total_interestThe total interest you will pay over the life of the loan is approximately $212,530.68.

Summary of Answers:

• a) You can afford a loan of $129,469.32.
• b) The total amount you will pay over 30 years is $342,000.
• c) The total interest paid will be $212,530.68.

Would you like further details or have any questions about these calculations?

Related questions:

1. How does the interest rate affect the loan amount you can afford?
2. What would the monthly payment be if you increased the loan term to 40 years?
3. How would your total interest change if the loan interest rate was reduced to 6%?
4. What are some strategies to reduce the total interest paid on a mortgage?
5. How can you calculate the loan amount if you have a different monthly payment or term?

Tip: If possible, try to make extra payments toward the principal each year. Even small additional payments can significantly reduce the total interest paid and shorten the loan term.