Lana borrows $24,000 to pay for college. The loan has a 10% interest rate that compounds monthly. She plans to pay off the loan in 10 years.

How much will she pay in total?


$38,901


$47,273


$51,877


$64,969

To determine how much Lana will pay in total, we need to use the formula for calculating the total amount paid on a loan with compounded interest:

\[
A = P \left(1 + \frac{r}{n}\right)^{nt}
\]

Where:
- $ A $ is the total amount to be paid (including interest).
- $ P $ is the principal amount (initial loan amount), which is $24,000.
- $ r $ is the annual interest rate (10% or 0.10).
- $ n $ is the number of times the interest compounds per year (monthly, so $ n = 12 $).
- $ t $ is the time in years (10 years).

### Step-by-step calculation:

\[
A = 24000 \left(1 + \frac{0.10}{12}\right)^{12 \times 10}
\]

Let's calculate it step by step.The total amount Lana will pay over the 10 years is approximately **$64,969**.

This matches the last option in the list.

Would you like more details or have any questions?

Here are 5 related questions to deepen your understanding:
1. What if the interest rate was 5% instead of 10%?
2. How much would Lana pay if she took 15 years to repay the loan instead of 10?
3. What is the difference between simple interest and compound interest?
4. How would the total payment change if the loan compounded annually instead of monthly?
5. Can Lana reduce the total interest paid by making extra payments?

**Tip:** Making additional payments on a loan can help reduce the total interest paid, as it lowers the principal faster.

Lana borrows $24,000 to pay for college. The loan has a 10% interest rate that compounds monthly. She plans to pay off the loan in 10 years. How much will she pay in total?

Learn how to calculate the total amount Lana will pay for her $24,000 college loan with a 10% interest rate that compounds monthly over 10 years. This problem involves using the compound interest formula and covers financial mathematics concepts. Suitable for students in Grades 10-12.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation