Hi phoenixchuck,
Break even time period is the amount of time we are interested in that would take you to recover your 5k investment into points to lower your rate. Other closing costs are irrelevent in this particular equation since you had to pay them no matter what (or in this case it looks like you had them covered by other means, great!). The formula to come to this number is simple in concept - add up the interest savings you are recieving each month due to the 5k investment in points, until you reach a sum of 5k. At this break even point, you have saved exactly as much money as you had invested into reducing your APR. Every month after this is money in your pocket.
The forumula is not (that) straightforward but still simple enough. Every month you are paying a slightly different ratio of interest and principal, my forumula accounts for that. I like looking at the break even point when rate shopping because it tells me how long I am locking myself into a rate before it pays for itself. That matters to me because I want to know what kind of refinancing options I have down the road. In your particular case where you paid 0 into points, you would need to refinance within the first 23 months of the loan before the decision not to pay 5k in points starts costing you more than the 5k you saved.
Anyone please chime in and correct me if I am wrong of course, I'm not an accountant, just a simple engineer =).
