Tom purchased a house in September 2022. His 30-year fixed mortgage loan started with the principal of $200,000 and 6% APR. His mortgage lender contacted him in September 2023 to check if he would like to refinance his mortgage loan since the mortgage rate dropped significantly in this year. There is no significant change on Tom's financials and credit score since he purchased the house, which may qualify him for 4% APR. The cost of refinancing including origination fee, appraisal , title, administration, etc. will be $ 12,000. With the interest rate drops , U.S. treasuries long-term rate has dropped to 2.5% as well.

QUESTION: The mortgage lender offers Tom to buy points and lower the APR. If Tom would like to pay $6,000, the APR can be lowered to 3.5% for his 30-year loan. Should Tom take the offer considering his 4 year plan of staying with the house? Again, Tom will have to keep the house for how many years to make the offer worthwhile?