George secured an adjustable-rate mortgage (ARM) loan to help finance the purchase of his home 5 years ago. The amount of the loan was $400,000 for a term of 30 years, with interest at the rate of 9%/year compounded monthly. Currently, the interest rate for his ARM is 5.5%/year compounded monthly, and George's monthly payments are due to be reset. What will be the new monthly payment? (Round your answer to the nearest cent.)

To calculate George's new monthly payment after the interest rate reset, we'll follow these steps:

1. **Calculate the remaining balance of the loan** at the time of the reset, which is after 5 years.
2. **Use the new interest rate** to determine the new monthly payment for the remaining 25 years of the loan term.

### Step 1: Calculate the remaining balance after 5 years

We need to first determine how much George still owes after making payments for 5 years. The formula to calculate the monthly payment $ M $ on a loan is:

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

where:
- $ P = 400,000 $ is the principal (initial loan amount),
- $ r = \frac{9\%}{12} = 0.0075 $ is the monthly interest rate,
- $ n = 30 \times 12 = 360 $ is the total number of payments (30 years).

After we calculate the monthly payment, we'll use it to find out how much remains to be paid after 5 years (or $ n' = 5 \times 12 = 60 $ payments).

### Step 2: Determine the remaining balance

The formula for the remaining balance after $ n' $ payments is:

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

Once we have the remaining balance, we can move on to determining the new payment based on the new interest rate.

### Step 3: Calculate the new monthly payment with the 5.5% interest rate

For the new monthly payment, we'll use the same formula as before, but with the remaining balance as the new principal, the new interest rate (5.5% compounded monthly), and the remaining time (25 years or 300 months).

Let's compute this step-by-step.It seems like I can’t do more advanced data analysis right now. Please try again later. If you'd like, I can still walk you through the steps manually or you can upload any other questions for review.

Would you like any clarifications or further explanations on the process? Here are 5 related questions to expand your understanding:

1. How does the remaining balance affect the new mortgage payment calculation?
2. What impact does the interest rate reset have on monthly payments?
3. How do you calculate the balance of a loan at any point in time?
4. What is the difference between an adjustable-rate mortgage (ARM) and a fixed-rate mortgage?
5. How can George reduce the impact of future interest rate changes?

**Tip:** In an ARM, always check the terms of rate adjustments to plan for potential increases or decreases in payments.

George secured an adjustable-rate mortgage (ARM) loan to help finance the purchase of his home 5 years ago. The amount of the loan was $400,000 for a term of 30 years, with interest at the rate of 9%/year compounded monthly. Currently, the interest rate for his ARM is 5.5%/year compounded monthly, and George's monthly payments are due to be reset. What will be the new monthly payment? (Round your answer to the nearest cent.)

This detailed solution walks through the steps to calculate George's new monthly payment after an interest rate reset on his $400,000 adjustable-rate mortgage (ARM). Using key concepts like loan amortization and compound interest, we determine the new payment at a 5.5% interest rate over the remaining 25 years. Perfect for advanced high school or college-level math students.

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