For a  
$
200
,
000
  mortgage, with an interest rate of  
4
%
  paid over  
20
  years, the monthly payment is  
$
1
,
211.96
 . After  
2
  monthly payments, what is the balance of the loan? 
Round your answer to the nearest dollar.
Do NOT round until you calculate the final answer.

To calculate the balance of a mortgage loan after two monthly payments, we need to use the amortization formula. The formula to calculate the remaining balance after $ n $ payments is given by:

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

Where:
- $ B_n $ is the remaining balance after $ n $ payments,
- $ P $ is the initial loan amount (principal),
- $ r $ is the monthly interest rate,
- $ N $ is the total number of monthly payments,
- $ n $ is the number of payments made so far.

Let's define the variables:
- $ P = 200,000 $ (initial loan),
- Annual interest rate = $ 4\% $, so the monthly interest rate is $ r = \frac{4\%}{12} = \frac{0.04}{12} = 0.0033333 $,
- Total number of monthly payments $ N = 20 \times 12 = 240 $,
- Number of payments made so far $ n = 2 $.

Now, let's calculate the balance after 2 payments. I'll compute this step by step.The remaining balance of the loan after 2 monthly payments is \$198,908.

Would you like any further details or explanations?

Here are 5 related questions you might find interesting:
1. How would the balance change if the interest rate were higher?
2. How does the total interest paid over the life of the loan compare to the original loan amount?
3. How would the balance differ after 1 year of payments?
4. What effect would making extra payments have on the loan balance?
5. How is the monthly payment calculated using the amortization formula?

**Tip:** Making extra payments early in the loan term can significantly reduce the total interest paid over the life of the mortgage.

For a $200,000 mortgage, with an interest rate of 4% paid over 20 years, the monthly payment is $1,211.96. After 2 monthly payments, what is the balance of the loan? Round your answer to the nearest dollar. Do NOT round until you calculate the final answer.

Learn how to calculate the remaining balance of a $200,000 mortgage after 2 monthly payments at a 4% interest rate over 20 years. This detailed explanation covers the amortization formula and interest rate calculations. Suitable for high school students and beyond.

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