Christina bought a new car for $28,000
. She paid a 20%
 down payment and financed the remaining balance for 72
 months with an APR of 6.5%
. Assuming she makes monthly payments, determine the total interest Christina pays over the life of the loan. Round your answer to the nearest cent, if necessary.



Let's go through the steps to determine the total interest Christina pays over the life of her car loan.

### Step 1: Calculate the down payment
Christina makes a 20% down payment on a car priced at $28,000.

\[
\text{Down payment} = 0.20 \times 28,000 = 5,600
\]

### Step 2: Calculate the loan amount
The remaining balance after the down payment is the amount she finances:

\[
\text{Loan amount} = 28,000 - 5,600 = 22,400
\]

### Step 3: Use the loan formula
The monthly payment for a loan is calculated using the following formula:

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

Where:
- $M$ = monthly payment
- $P$ = loan amount ($22,400)
- $r$ = monthly interest rate (APR divided by 12 months)
- $n$ = number of payments (72 months)

The APR is 6.5%, so the monthly interest rate is:

\[
r = \frac{6.5\%}{12} = \frac{0.065}{12} = 0.0054167
\]

### Step 4: Plug in the values
Now, substitute the values into the formula to calculate the monthly payment $M$.

\[
M = \frac{22,400 \times 0.0054167 \times (1 + 0.0054167)^{72}}{(1 + 0.0054167)^{72} - 1}
\]

Let's calculate the monthly payment $M$ first.

The monthly payment Christina will make is approximately $376.54.

### Step 5: Calculate the total amount paid over the life of the loan
To find the total amount paid, multiply the monthly payment by the number of months:

\[
\text{Total payments} = 376.54 \times 72 = 27,911.04
\]

### Step 6: Calculate the total interest paid
The total interest paid is the total amount paid over the life of the loan minus the original loan amount:

\[
\text{Total interest} = 27,911.04 - 22,400 = 5,511.04
\]

### Final Answer:
Christina will pay approximately **$5,511.04** in interest over the life of the loan.

Would you like more details or have any questions?

Here are five related questions:
1. What if the APR was 5% instead of 6.5%?
2. How does the length of the loan (number of months) affect the total interest paid?
3. What is the impact of making a larger down payment on the total interest?
4. How would bi-weekly payments instead of monthly ones affect the total interest?
5. How much interest would Christina save if she paid off the loan early?

**Tip:** Reducing your loan term or increasing your monthly payments can significantly decrease the total interest paid over time!

Christina bought a new car for $28,000. She paid a 20% down payment and financed the remaining balance for 72 months with an APR of 6.5%. Assuming she makes monthly payments, determine the total interest Christina pays over the life of the loan. Round your answer to the nearest cent, if necessary.

Determine the total interest Christina pays on her car loan of $28,000 with a 20% down payment and 72-month financing at 6.5% APR. This solution uses loan amortization formulas to calculate monthly payments and total interest. Suitable for high school students learning finance concepts.

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