Here's the math, assuming a standard fixed-rate loan with monthly payments. The payment at 6.75% is about $2,594.39 and at 6.25% about $2,462.85, so the points save about $131.54 a month.
Break-even: $8,000 divided by $131.54 is about 61 months, or just over 5 years. Sell before then and you lose money on the points.
At 7 years (84 months): Cash paid is about $3,049 less with the points, after subtracting the $8,000. The lower-rate loan also owes about $3,036 less on the balance, so your net position is about $6,085 better, before any sale costs.
That figure ignores what the $8,000 could have earned if you kept it. Compounded over 7 years, the points stop paying off at a return of roughly 8.4% a year. The best return is the one you could get on the money for the same risk. Whether points make sense also depends on the tax treatment of points, which a tax professional can check for your situation, and on whether you might refinance or move sooner.
