A $525,000 adjustable rate mortgage is expected to have the following payments:


Year	Interest Rate	Monthly Payment
1–5	4%	$2,506.43
6–15	6%	$3,059.46
16–25	8%	$3,464.78
26–30	10%	$3,630.65


A fixed-rate mortgage in the same amount is offered with an interest rate of 4.65%.

What is the difference in the total cost between the two mortgages, rounded to the nearest dollar?

A spreadsheet was used to calculate the correct answer. Your answer may vary slightly depending on the technology used.

To determine the difference in the total cost between the adjustable rate mortgage (ARM) and the fixed-rate mortgage, we need to calculate the total cost of both mortgages and then find the difference.

### Adjustable Rate Mortgage (ARM)
The total cost for the ARM is the sum of all the payments over the 30-year period. We'll calculate the total payment for each period and then sum them up.

1. **Years 1–5 (4% interest rate):**
   - Monthly payment: $2,506.43
   - Number of payments: $5 \times 12 = 60$
   - Total cost: $60 \times 2,506.43$

2. **Years 6–15 (6% interest rate):**
   - Monthly payment: $3,059.46
   - Number of payments: $10 \times 12 = 120$
   - Total cost: $120 \times 3,059.46$

3. **Years 16–25 (8% interest rate):**
   - Monthly payment: $3,464.78
   - Number of payments: $10 \times 12 = 120$
   - Total cost: $120 \times 3,464.78$

4. **Years 26–30 (10% interest rate):**
   - Monthly payment: $3,630.65
   - Number of payments: $5 \times 12 = 60$
   - Total cost: $60 \times 3,630.65$

### Fixed-Rate Mortgage (4.65% interest rate)
The fixed-rate mortgage has a constant monthly payment for 30 years. We'll first calculate the monthly payment using the mortgage formula, then determine the total cost.

The formula for the monthly payment $ M $ on a fixed-rate mortgage is:

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

Where:
- $ P = 525,000 $ (loan amount)
- $ r = \frac{4.65\%}{12} = \frac{0.0465}{12} \approx 0.003875 $ (monthly interest rate)
- $ n = 30 \times 12 = 360 $ (total number of payments)

### Step 1: Calculate the Monthly Payment for the Fixed-Rate Mortgage

Let's compute these values.The monthly payment for the fixed-rate mortgage at 4.65% interest is approximately $2,707.09.

### Step 2: Calculate the Total Cost for Each Mortgage

Now, we'll compute the total costs for both the adjustable rate mortgage (ARM) and the fixed-rate mortgage.

- **ARM Total Cost**:
  - Years 1–5: $ 60 \times 2,506.43 = 150,385.8 $
  - Years 6–15: $ 120 \times 3,059.46 = 367,135.2 $
  - Years 16–25: $ 120 \times 3,464.78 = 415,773.6 $
  - Years 26–30: $ 60 \times 3,630.65 = 217,839 $

- **Fixed-Rate Total Cost**:
  - $ 360 \times 2,707.09 $

Let's calculate these values.### Step 3: Calculate the Difference

- **Total cost of the Adjustable Rate Mortgage (ARM)**: $1,151,134
- **Total cost of the Fixed-Rate Mortgage**: $974,554

Finally, the difference in the total cost between the two mortgages is:

\[
\text{Difference} = 1,151,134 - 974,554 = 176,580
\]

### Answer:
The difference in the total cost between the two mortgages is **$176,580**.

Would you like further details, or do you have any questions?

Here are some related questions you might find interesting:
1. How does changing the loan term affect the monthly payments?
2. What would be the impact of making additional payments on the ARM?
3. How does the difference in total cost change with a higher fixed interest rate?
4. What are the advantages and disadvantages of an adjustable-rate mortgage compared to a fixed-rate mortgage?
5. How would the total cost change if the interest rates for the ARM were different?

**Tip:** Always consider the possibility of interest rate changes in an ARM when comparing it to a fixed-rate mortgage.

A $525,000 adjustable rate mortgage is expected to have the following payments: 
Year Interest Rate Monthly Payment 
1–5 4% $2,506.43 
6–15 6% $3,059.46 
16–25 8% $3,464.78 
26–30 10% $3,630.65 
A fixed-rate mortgage in the same amount is offered with an interest rate of 4.65%. What is the difference in the total cost between the two mortgages, rounded to the nearest dollar?

This page provides a detailed comparison between a $525,000 adjustable rate mortgage with varying interest rates over a 30-year period and a fixed-rate mortgage at 4.65%. Learn how to calculate the total cost for both options using mortgage formulas and understand the $176,580 cost difference.

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