You decide to finance a $15,000.00 car at a 5% interest rate for 6 years.

A. How much will your monthly payment?

B. By the end of the loan what will be the total of all your payments?

C. How much interest will you pay over the life of the loan?


To solve this, we will use the **loan amortization formula** for monthly payments on a fixed-rate loan. The formula for the monthly payment $ M $ is:

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

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

### Given dataTo solve this, we will use the **loan amortization formula** for monthly payments on a fixed-rate loan. The formula for the monthly payment $ M $ is:

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

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

### Given 
- Loan amount $ P = 15,000 $,
- Annual interest rate = 5%, so the monthly interest rate $ r = \frac{5\%}{12} = 0.004167 $,
- Loan term = 6 years, which is $ 6 \times 12 = 72 $ months.

#### Part A: Calculate the monthly payment.
Let me calculate this for you.### A. The monthly payment will be approximately **$241.57**.

Now, let's calculate the total amount of all payments and the total interest paid over the life of the loan.

#### Part B: The total of all payments over the life of the loan is:
\[
\text{Total Payments} = M \times n
\]
Let me calculate that now.### B. The total of all payments by the end of the loan will be approximately **$17,393.33**.

#### Part C: To find the total interest paid over the life of the loan:
\[
\text{Total Interest} = \text{Total Payments} - P
\]
Let me calculate that now.### C. The total interest paid over the life of the loan will be approximately **$2,393.33**.

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Would you like more details or have any further questions? Here are some related questions for practice:

1. What would the monthly payment be if the loan term was only 4 years?
2. How would the monthly payment change if the interest rate increased to 7%?
3. What is the total interest paid if you shorten the loan term to 3 years with the same interest rate?
4. How much would the monthly payment be for a $20,000 car under the same terms?
5. How much total interest would you save by making a $500 extra payment each year?

**Tip:** Making extra payments toward the loan principal can significantly reduce the total interest paid.

You decide to finance a $15,000.00 car at a 5% interest rate for 6 years.

A. How much will your monthly payment?

B. By the end of the loan what will be the total of all your payments?

C. How much interest will you pay over the life of the loan?

Learn how to calculate monthly payments for a $15,000 car loan with a 5% interest rate over 6 years. Discover how much you'll pay each month, the total cost of the loan, and the interest paid over time. This is ideal for high school students or anyone looking to understand loan amortization.

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