You take out a car loan for $8000 at 7% intrest, compounded monthly. Your monthly payment is $93. How long will it take you to pay off the loan, and how much will you pay it total?


To solve this problem, we can use the formula for the monthly payment on a loan with compounded interest:

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

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

Given:
- $ P = 8000 $,
- Annual interest rate = 7%, so monthly rate $ r = \frac{0.07}{12} = 0.005833 $,
- $ M = 93 $.

We need to solve for $ n $, the number of months to fully pay off the loan.

### Rearranging the formula:
\[
M = P \frac{r(1+r)^n}{(1+r)^n - 1}
\]

Solving for $ n $:

\[
93 = 8000 \times \frac{0.005833 \times (1 + 0.005833)^n}{(1 + 0.005833)^n - 1}
\]

Let's compute $ n $ using this formula.It will take approximately 120 months (or 10 years) to pay off the loan.

The total amount paid over this period will be approximately \$11,140.36.

Would you like further clarification or a detailed breakdown of the steps?

Here are some related questions:
1. What happens if you increase your monthly payment?
2. How would the total cost change with a higher interest rate?
3. Can you pay off the loan faster without increasing monthly payments?
4. What portion of the total payment is interest?
5. How does the loan term affect the total interest paid?

**Tip:** Increasing your monthly payments, even slightly, can significantly reduce the total interest paid over time.

You take out a car loan for $8000 at 7% interest, compounded monthly. Your monthly payment is $93. How long will it take you to pay off the loan, and how much will you pay in total?

Learn how to calculate the time to pay off a car loan of $8000 at 7% interest compounded monthly with $93 monthly payments. This detailed solution uses loan amortization and compound interest formulas. Ideal for high school students in Grades 10-12.

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