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 $250,000 for a term of 30 years, with interest at the rate of 6%/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 the new monthly payment for George after the interest rate reset, we'll follow these steps:

1. **Determine the remaining balance of the loan after 5 years.**
2. **Calculate the new monthly payment based on the new interest rate and the remaining loan balance.**

### Step 1: Find the remaining balance after 5 years
The initial loan amount was $250,000, with a 30-year term and an interest rate of 6% compounded monthly. The formula for calculating the monthly payment $ M $ is:

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

Where:
- $ P = 250,000 $ (the principal loan amount),
- $ r = \frac{0.06}{12} = 0.005 $ (monthly interest rate),
- $ n = 30 \times 12 = 360 $ (total number of payments over 30 years).

We first need to calculate the original monthly payment, then find the remaining balance after 5 years (60 payments).

The remaining balance $ B $ after making $ t $ payments is given by:

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

Where $ t = 60 $ (since 5 years of payments have been made).

### Step 2: Find the new monthly payment
With the remaining balance found, the new monthly payment under the 5.5% interest rate can be calculated using the same monthly payment formula, but this time with the updated interest rate and remaining loan term.

Let's go ahead and compute this.1. **Initial Monthly Payment**: George's original monthly payment was approximately \$1,498.88.

2. **Remaining Balance After 5 Years**: After making payments for 5 years, the remaining balance on the loan is approximately \$232,635.89.

3. **New Monthly Payment**: With the new interest rate of 5.5%, the new monthly payment will be approximately \$1,428.59.

Would you like more details or have any questions?

Here are five related questions:
1. How do adjustable-rate mortgages differ from fixed-rate mortgages?
2. What are the risks involved in taking an adjustable-rate mortgage (ARM)?
3. How is the remaining balance on a loan calculated after partial payments?
4. How does a lower interest rate impact the overall cost of a loan?
5. What are the pros and cons of refinancing a mortgage?

**Tip**: Regularly checking interest rates and considering refinancing can save you significant money on long-term loans like mortgages.

Calculate the new monthly payment for a $250,000 adjustable-rate mortgage (ARM) after 5 years with an interest rate reset from 6% to 5.5%. This example uses loan amortization formulas to determine the remaining balance and the new monthly payment. Ideal for students and professionals looking to understand mortgage payment calculations.

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