Question

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 4.85%.

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.
$159,134
$153,796
$901,409
$668,123

Answer 1

The difference in total cost between the adjustable-rate mortgage and the fixed-rate mortgage is approximately $892,834.

Step-by-step explanation:

To find the difference in total cost between the adjustable-rate mortgage and the fixed-rate mortgage, we need to calculate the total payments for each mortgage.

For the adjustable-rate mortgage, we can add up the monthly payments for each time period:

1. 1-5 years: $2,506.43 x 5 = $12,532.15
2. 6-15 years: $3,059.46 x 10 = $30,594.60
3. 16-25 years: $3,464.78 x 10 = $34,647.80
4. 26-30 years: $3,630.65 x 5 = $18,153.25

So the total cost of the adjustable-rate mortgage is $12,532.15 + $30,594.60 + $34,647.80 + $18,153.25 = $95,927.80.

For the fixed-rate mortgage, we need to calculate the monthly payment using the loan amount and the interest rate. Using the formula:

Monthly Payment = Loan Amount x Monthly Interest Rate / (1 - (1 + Monthly Interest Rate)-Number of Payments).

Substituting the values, we get:

Loan Amount = $525,000

Interest Rate = 4.85% / 100 = 0.0485

Number of Payments = 30 years x 12 months/year = 360

Monthly Interest Rate = 0.0485 / 12 = 0.004042

Plugging these values in, the monthly payment for the fixed-rate mortgage is approximately $2,746.56.

So the total cost of the fixed-rate mortgage is $2,746.56 x 360 = $988,761.60.

The difference in total cost between the two mortgages is $988,761.60 - $95,927.80 = $892,833.80.

Rounded to the nearest dollar, the difference in total cost is $892,834.