**William M: **‘I’m pretty ignorant about mortgages. I know that a point equals one percent, so that on a $300,000 mortgage, one point equals a $3,000 up-front payment. But I’m not sure if I want to pay points to get a lower rate. Which of these six mortgage options I’ve been offered for a 30-year, fixed-rate mortgage on a new house makes the most sense?’

$300,000 30-year Fixed Mortgage

Interest Rate | Points in % | Points in $ |

6.000% | 2.625 | $7,875 |

6.125% | 2.000 | $6,000 |

6.250% | 1.250 | $3,750 |

6.375% | 0.750 | $2,250 |

6.500% | 0.250 | $750 |

6.625% | 0.000 | $0 |

☞ It comes down to a judgment call: how long will you keep this loan in force before you either sell the home or refinance the loan? **The longer you think you’ll keep this mortgage, the more reason you have to pay up-front points to get a lower interest rate.**

But this is an odd progression they’re offering you, isn’t it? For each extra eighth of a percent in annual interest you are willing to pay, you’d expect to save roughly the same amount in points. Yet at the first break you save 5 eighths of a point, then 6 eighths, then 4 then 4 then 2. Not sure why they do that.

Right? I’ve added the column in red to show the difference in dollars.

If you were willing to pay 6.125% interest instead of 6% – an eighth of a percent more – you’d pay just $6,000 in points versus $7,875, saving $1,875. Whereas (at the other end of the progression), if you agreed to pay 6.625% instead of 6.5%, you would save just $750.

Why would you agree to 6.625% rather than 6.5% – when doing so saves you only 2 eighths of a point? That would only make sense if you planned to keep the loan for less than two years. **And if you think you will only be in this house for two years, don’t buy it – rent something.**

If you plan to keep this mortgage in force for a long time, then you want to pay the points in order to get the lower rate . . . even when you have to pay 6 eighths of a point up front in order to save just 1 eighth of a point a year for 30 years. You ‘break even’ in this situation after 6 years, and then enjoy 24 years of additional savings, assuming you hang on to the loan until it is fully paid off.

Admittedly, there are a few wrinkles to consider. Wrinkles are orange. Feel free to meet me a few paragraphs down, when we’re back in the black.

- One wrinkle is the tax-deductibility of the points. This is a new mortgage, so the points are deductible up-front and you’re comparing apples and apples – both the points and the mortgage interest are deductible.

- But if it were a refinance, the points would only be deductible over the life of the mortgage (with any remaining undeducted points deductible all at once if you sell or pay off the mortgage early). And that would make the points more expensive, giving you more reason not to want to pay them.

- A second wrinkle is the time value of money. Clearly, paying 6 eighths of a point now to save 1 eighth of a point a year for 6 years isn’t really a break-even situation, as I described it above. Who in his right mind, given the choice between $6 now and a $1 a year for 6 years would choose the latter? Money now is more valuable than money in the future. (A bird in the hand, and all that.)

- Depending on where you set your “discount rate” – which is a measure of the importance you place on having money now versus waiting for it – you could come up with a very specific breakeven point. “So long as I hold the mortgage at least 7.4 years,” you might calculate, “it makes sense to pay 6 eighths of a point now to save 7.4 eighths over 7.4 years. Anything beyond that will be gravy.” Let’s leave your discount rate for another column. But the sense of it is this: If you are desperate for money, or have fantastically profitable things you can do with it (like pay off an 18% credit card), you will have a high discount rate, and place a great premium on saving money up front, even if it means higher payments for many years to come. If, on the other hand, you really don’t have that much you need the money for – you figure it would just sit in Treasuries earning 4% – then your personal “discount rate” would be low, and you’d be more inclined to pay the points in order to enjoy a lower interest rate going forward.

- The final wrinkle (or at least the final one that occurs to me) is that you are not really borrowing $300,000 for 30 years, so figuring the precise breakeven point is even more complicated. You are borrowing $300,000 to begin with, but each month you are paying down the principal – imperceptibly at first, but then a little more each year. So those last 10 years of a 30-year mortgage are really pretty insignificant when it comes to this decision, for two reasons, First, as I say, the time value of money – $1 saved 25 years from now sure ain’t worth paying $1 for now. (More like 12 cents, if you use a 9% discount rate.) Second, after 25 years on a conventional 30-year 6.5% $300,000 mortgage you are not borrowing $300,000; your outstanding principal is down to under $90,000. So the eighth of a point you’re saving in year 25 doesn’t save you $375, as it did the first year, but just $112.50.

- These wrinkles can be of an interest to a math major. But since you don’t know how long you’ll hold your mortgage, it’s a level of complexity you can comfortably ignore.

**As a practical matter, William, faced with this grid of options, you should probably take the 6.25% choice, which is the low-hanging fruit – it costs you very little up front to lower your rate by 3 eighths of a point. If you keep the loan even just 4 years, let alone 30, you will come out ahead.**