If you take out a  
$
8
,
000
  loan for a period of  
6
  months at an  
8
%
  interest rate, what will your outstanding balance be after two monthly payments? Round your answer to the nearest cent as necessary and do not include the dollar sign.

We can solve this using the amortization formula for loan payments. Here's how to break it down:

The loan amount ($P$) is $8,000, the interest rate ($r$) is 8% per year (which is $0.08$), and the loan term ($n$) is 6 months.

We need to calculate the monthly payment first, using the formula for a loan payment:

\[
M = \frac{P \cdot \left( \frac{r}{12} \right)}{1 - \left(1 + \frac{r}{12}\right)^{-n}}
\]

Where:
- $P$ is the loan amount ($8,000),
- $r$ is the annual interest rate (8%),
- $n$ is the number of months (6 months).

Then, we calculate the remaining balance after two payments. Let me work through this calculation.After two monthly payments, the outstanding balance on the loan will be approximately **5368.69**.

Would you like further details on the calculation, or do you have any other questions?

Here are 5 related questions:
1. How is the amortization formula derived?
2. What happens if the interest rate changes during the loan term?
3. How can you calculate the total interest paid on a loan?
4. What effect does extending the loan period have on monthly payments?
5. How does compound interest differ from simple interest in loans?

**Tip:** Making extra payments on a loan can significantly reduce the total interest paid over time.

If you take out a $8,000 loan for a period of 6 months at an 8% interest rate, what will your outstanding balance be after two monthly payments? Round your answer to the nearest cent as necessary and do not include the dollar sign.

Learn how to calculate the outstanding balance on an $8,000 loan after two monthly payments with an 8% annual interest rate. This problem involves using the amortization formula to determine the balance remaining after two months in a 6-month loan term. Ideal for students in Grades 10-12.

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