Final answer:
The mortgage with points would be a better option if you plan to stay in the house for at least 30 years, as it would save you approximately $580.34 over the 30-year period compared to the mortgage without points.
Step-by-step explanation:
To determine how long you would have to stay in the house for the mortgage with points to be a better option, we need to compare the total costs of each mortgage option over a specific time period.
Let's assume that the discount point costs 1% of the loan amount, which is $1,000 ($100,000 * 1%).
The total cost of the mortgage without points can be calculated using the formula:
Total Cost = Loan Amount * (1 + Interest Rate)^Time - Loan Amount
Using this formula, the total cost of the mortgage without points over 30 years would be:
Total Cost = $100,000 * (1 + 0.06)^30 - $100,000 = $389,926.76
The total cost of the mortgage with points can be calculated by adding the discount point cost to the loan amount and then using the same formula:
Total Cost = (Loan Amount + Discount Point Cost) * (1 + Interest Rate)^Time - (Loan Amount + Discount Point Cost)
Using this formula, the total cost of the mortgage with points over 30 years would be:
Total Cost = ($100,000 + $1,000) * (1 + 0.0575)^30 - ($100,000 + $1,000) = $389,346.42
Therefore, the mortgage with points would be a better option if you plan to stay in the house for at least 30 years, as it would save you approximately $580.34 over the 30-year period compared to the mortgage without points.