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The image you uploaded shows a problem involving loan amortization. Let’s break down each part and solve it step-by-step.

### Given Information:
- **Loan Amount (P):** $5000
- **APR (Annual Percentage Rate):** 9% (r = 0.09 as a decimal)
- **Time (t):** 2 years (24 months)
- **Monthly Interest Rate (r):** $\frac{0.09}{12} = 0.0075$

The monthly payment formula is given as:

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

#### Part (a) - What is your monthly payment?
We need to calculate the monthly payment $M$.

Let’s plug in the values:

- $ P = 5000 $
- $ r = 0.0075 $
- $ t = 24 $ months

Now I’ll compute this for you.The monthly payment is approximately **$228.42**.

#### Part (b) - Total Amount Paid and Interest:

1. **Total amount paid to the bank**:
   \[
   \text{Total paid} = M \times t
   \]
2. **Total interest paid**:
   \[
   \text{Interest} = \text{Total paid} - P
   \]

Let me calculate these now.It seems like I can’t do more advanced data analysis right now. Please try again later.

However, I can guide you through the process so you can compute the remaining steps manually.

#### Part (b) - Total Amount Paid and Interest:
1. **Total amount paid to the bank**:
   \[
   \text{Total paid} = M \times t = 228.42 \times 24 = 5482.08
   \]

2. **Total interest paid**:
   \[
   \text{Interest} = \text{Total paid} - P = 5482.08 - 5000 = 482.08
   \]

So, you would have paid a total of **$5482.08**, with **$482.08** of that amount being interest.

#### Part (c)(i) - How much do you still owe after 1 year (12 payments)?
Use the formula for the balance after $k$ payments:
\[
B = P \times \frac{(1 + r)^t - (1 + r)^k}{(1 + r)^t - 1}
\]
For 12 payments, plug in the values:
- $k = 12$
- $r = 0.0075$
- $t = 24$

You can plug these values into the formula to find the remaining balance after 1 year.

Would you like more details, or should we discuss further steps?

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Here are 5 related questions to expand your understanding:
1. What happens to the interest if you increase the loan term to 3 years?
2. How would a change in the APR from 9% to 7% affect the monthly payment?
3. What is the remaining balance after making 18 monthly payments?
4. Can you pay off the loan early, and how does that affect the total interest paid?
5. What is the amortization schedule, and how can you use it for financial planning?

**Tip:** Always review the interest rate and loan term before committing to a loan, as these directly impact the total interest you'll pay.

Suppose you borrow $5000 at a monthly interest rate of r = 0.0075 and wish to pay off the loan in 24 months. Calculate the monthly payment, total amount paid, interest paid, amount still owed after 12 payments, and complete the amortization table.

Learn how to calculate the monthly payment, total paid, and remaining balance after 12 months for a $5000 loan at 9% APR over 2 years. Includes a step-by-step solution for the amortization schedule and interest calculations.

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