Final answer:
To determine the better mortgage option for the buyer, we need to compare the total cost of each option. Option 1 has a fixed interest rate of 4% for a 30-year term, while Option 2 has a fixed interest rate of 3.75% for a 30-year term with a $10,000 upfront fee to buy down the rate. By calculating the total cost of each option, we find that Option 2 has a lower total cost, making it the better choice for the buyer.
Step-by-step explanation:
To determine which mortgage option is better for the buyer, we need to compare the total cost of each option. Option 1 has a fixed interest rate of 4% for a 30-year term, while Option 2 has a fixed interest rate of 3.75% for a 30-year term with a $10,000 upfront fee to buy down the rate.
Let's calculate the total cost of Option 1 first. The total cost can be found using the formula:
Total Cost = Loan Amount + Total Interest Paid
The loan amount is 80% of $625,000, which is $500,000. The total interest paid can be calculated using the formula:
Total Interest Paid = (Loan Amount) * (Interest Rate) * (Loan Term)
Substituting the values, we get:
Total Interest Paid = $500,000 * 0.04 * 30 = $600,000
Therefore, the total cost of Option 1 is:
Total Cost = $500,000 + $600,000 = $1,100,000
Next, let's calculate the total cost of Option 2. The loan amount is the same as Option 1, $500,000. The total interest paid can be calculated using the same formula:
Total Interest Paid = $500,000 * 0.0375 * 30 = $562,500
However, there is also an upfront fee of $10,000. Therefore, the total cost of Option 2 is:
Total Cost = $500,000 + $562,500 + $10,000 = $1,072,500
Option 2 has a lower total cost compared to Option 1. Therefore, Option 2, because it reduces the overall cost, is better for the buyer.