Final answer:
The better mortgage option for Alice can be determined by calculating the total cost of each option, including the interest paid over 30 years, and comparing them. This requires applying the 4% and 3.75% interest rates to the loan amount after her 20% deposit and adding the $10,000 fee to the latter option.
Step-by-step explanation:
To determine which mortgage option is better for the buyer, Alice, it's important to compare the total cost of each loan over the life of the 30-year term, taking into account her 20% deposit on a $625,000 house.The first option is a 30-year term with a fixed interest rate of 4%. For the second option, she pays a $10,000 upfront fee to buy down the rate to 3.75% for the same termTo decide which is more cost-effective, one would need to calculate the total interest paid over the life of the loan for both scenarios and add the $10,000 upfront fee to the total cost of the second option. This calculation would require knowing the loan amount after the down payment, which is 80% of $625,000, and applying the respective interest ratesFor example, if the loan amount is $500,000, the total interest paid at 4% over 30 years is different than at 3.75% with an additional $10,000 fee.
It is essential to perform these calculations to see which total payment is lower, indicating the better option for the buyer.When comparing the two mortgage options, it's important to consider the total cost of each option over the term of the loan. Let's calculate the total cost of each option for Alice.Option 1: With a fixed interest rate of 4% and a 30-year term, Alice would pay interest of 4% of the balance each year. The initial mortgage balance would be $625,000 - 20% deposit = $500,000. So, the first-year interest payment would be $500,000 * 0.04 = $20,000. Over 30 years, Alice would end up paying $20,000 * 30 = $600,000 in interest.Option 2: By paying a $10,000 upfront fee to buy down the interest rate to 3.75%, Alice would reduce the annual interest payment. Using the same initial mortgage balance of $500,000, the first-year interest payment would be $500,000 * 0.0375 = $18,750. Over 30 years, Alice would pay $18,750 * 30 = $562,500 in interest.Therefore, the better option for the buyer is Option 2 because it would result in lower interest payments over the 30-year term.