Question

A $225,000 adjustable-rate mortgage is expected to have the following payments:


Year Interest Rate Monthly Payment
1–5 4% $1,074.18
6–15 6% $1,311.20
16–25 8% $1,484.91
26–30 10% $1,555.99


A fixed-rate mortgage in the same amount is offered for 30 years and 7% interest.

Part A: What is the total cost of the adjustable-rate mortgage? State which technology or method you used. Show or explain all steps. (3 points)

Part B: What is the total cost of the fixed-rate mortgage? State which technology or method you used. Show or explain all steps. (3 points)

Part C: Using your values from parts A and B compare the advantages and disadvantages of the two loan types. (4 points)

Answer 1

This is my answer

Answer 2

Part A: To calculate the total cost of the adjustable-rate mortgage, we need to add up all the monthly payments for each period.

For the first 5 years:
Total cost = $1,074.18 * 12 months/year * 5 years = $64,450.80

For the next 10 years:
Total cost = $1,311.20 * 12 months/year * 10 years = $157,344.00

For the next 10 years:
Total cost = $1,484.91 * 12 months/year * 10 years = $178,189.20

For the final 5 years:
Total cost = $1,555.99 * 12 months/year * 5 years = $93,359.40

Adding all these costs together:
Total cost of the adjustable-rate mortgage = $64,450.80 + $157,344.00 + $178,189.20 + $93,359.40 = $493,343.40

I used simple multiplication to calculate the total cost of the adjustable-rate mortgage.

Part B: To calculate the total cost of the fixed-rate mortgage, we use the formula for a fixed-rate mortgage:

Total cost = Monthly payment * 12 months/year * 30 years

Total cost = $1,622.27 * 12 months/year * 30 years = $584,017.20

I used simple multiplication to calculate the total cost of the fixed-rate mortgage.

Part C:

Advantages of adjustable-rate mortgage:
- Lower initial monthly payments, making it more affordable in the short term
- Potential for lower interest rates and payments in the future if interest rates decrease

Disadvantages of adjustable-rate mortgage:
- Payments can increase significantly if interest rates rise
- Uncertainty about future payments can make budgeting difficult

Advantages of fixed-rate mortgage:
- Predictable monthly payments for the entire term of the loan
- Protection against rising interest rates

Disadvantages of fixed-rate mortgage:
- Higher initial interest rate compared to adjustable-rate mortgage
- Higher total cost over the life of the loan

In this case, the adjustable-rate mortgage has a lower total cost compared to the fixed-rate mortgage. However, it also comes with the risk of increasing payments if interest rates rise. The fixed-rate mortgage offers predictability and protection against rising interest rates, but at the cost of a higher total repayment amount. Ultimately, the choice between the two loan types will depend on individual preferences and risk tolerance.