The problem asks for the savings between two types of mortgages: a 30-year mortgage and a 15-year mortgage. Let's break this down:

Given Information:

• 30-year mortgage:

  • Loan amount: $200,000
  • Interest rate: 4.5%
  • Monthly payment: $1,020
  • Loan term: 30 years

• 15-year mortgage:

  • Loan amount: $200,000
  • Interest rate: 4.0%
  • Monthly payment: $1,480
  • Loan term: 15 years

Step 1: Total Payment for the 30-Year Mortgage

The total payments over the life of the 30-year mortgage is: $\text{Total payments for 30-year mortgage} = 1,020 \times 12 \times 30 = 367,200$

Step 2: Total Payment for the 15-Year Mortgage

The total payments over the life of the 15-year mortgage is: $\text{Total payments for 15-year mortgage} = 1,480 \times 12 \times 15 = 266,400$

Step 3: Calculate the Savings

The savings by opting for the 15-year mortgage instead of the 30-year mortgage is: $\text{Savings} = 367,200 - 266,400 = 100,800$

So, the 15-year fixed-rate mortgage would save you $100,800 over the length of both loans.

Correct Answer:

The correct choice is d) $100,800.

Would you like more details or explanations on how this was calculated?

Follow-Up Questions:

1. What is the difference in interest rates between a 30-year and 15-year mortgage in general?
2. How does a shorter loan term affect the total interest paid?
3. Why are the monthly payments higher for a 15-year mortgage even though the interest rate is lower?
4. How does the total loan amount affect your decision between different mortgage terms?
5. Can extra payments on a 30-year mortgage help you save money similar to a 15-year mortgage?

Tip:

Paying off your mortgage earlier reduces the total interest paid over time, leading to significant long-term savings.