You are considering taking a student loan for $10,000.00 that will be paid back 10 years at 2.2% compounded monthly, and will make monthly payments of $92.91. (Round all answers to 2 decimal places.)

What is the unpaid balance after 12 months?

To calculate the unpaid balance after 12 months for a loan with monthly compounded interest, we can use the formula for the remaining balance on a loan, which is:

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

Where:
- $ B_n $ = Unpaid balance after $n$ months
- $ P $ = Principal loan amount (initial loan), which is $10,000.00
- $ r $ = Monthly interest rate (annual interest rate divided by 12)
- $ n $ = Number of months passed (12 months in this case)
- $ M $ = Monthly payment ($92.91)

### Step-by-step:
1. **Find the monthly interest rate:**
   \[
   r = \frac{2.2\%}{12} = \frac{0.022}{12} = 0.0018333
   \]
2. **Use $n = 12$, $M = 92.91$, and $P = 10,000$** in the formula:
   \[
   B_{12} = 10,000(1 + 0.0018333)^{12} - \frac{92.91 \left((1 + 0.0018333)^{12} - 1 \right)}{0.0018333}
   \]

Now I'll compute this for you.The unpaid balance after 12 months is approximately **$9,096.00**.

Would you like further clarification or details on any step? Here are 5 related questions to consider:

1. How would the balance change if the interest rate was higher?
2. What if you made extra payments on top of the monthly $92.91?
3. How does compounding frequency affect the total interest paid over the loan period?
4. Can you calculate the total interest paid over the full 10-year loan?
5. How much would the monthly payment be if the loan term was reduced to 5 years?

**Tip:** Making additional payments early in the loan term can significantly reduce the amount of interest you pay over time.

You are considering taking a student loan for $10,000.00 that will be paid back 10 years at 2.2% compounded monthly, and will make monthly payments of $92.91. What is the unpaid balance after 12 months?

Learn how to calculate the unpaid balance after 12 months for a $10,000 loan at 2.2% interest compounded monthly. This problem involves key concepts such as loan amortization, compound interest, and monthly payments. A step-by-step solution is provided, suitable for college-level students.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation