# Calculating Future and Present value into mortgage comparisons

I'm looking to buy a home in the next 3 or 4 months. The bank I'm working with has 10 different mortgage rates, currently ranging from 3.5% to 4.625%, with points respectively ranging from 2.875 to -1.875 (see link).

I've created a spreadsheet that will add the up front costs associated with the points and the total payments over the life of the 30 year mortgage. This gives me a total cost of the mortgage, making it fairly obvious I'm better off paying points now and having lower monthly payments.

However, I started thinking that on one end I'm paying \$7k in points for the lower interest rate and lower monthly payment, where on the other end I receive \$4.5k from negative points, paying \$160 more per month (assuming \$250k mortgage). This got me wondering whether I'm better off taking the negative points lump sum difference and investing that over the 30 years, or paying the points and investing the additional \$160 per month.

Assuming I would get the same rate of return over the 30 years (say 5 or 6% invested in a stock index), how would I incorporate this into my spreadsheet? I initially used FV = P(1+r)^t for the lump sum and Excel's FV function for the \$160 monthly. Is that correct though? Or should I take the lump sum at face value and calculate present value of the \$160 paid monthly.

I really think modelling this correctly will save me thousands with not much work. However, I'm not sure I'm modelling this correctly. Any thoughts?

Keep in mind the number of months or years before you break even. You pay money to lower the interest rate, and lower the monthly cost. But it takes a number of months, using your numbers \$7,000 to save \$160 a month will take ~43 months. That is before figuring in the future or present value.

If you sell or refinance the mortgage, the initial points to lower the rate is gone.

• Good point. This is assuming we'll be in the house 15-20 years minimum.
– jas
Feb 2, 2012 at 17:50

You mentioned 15-20 years in your comment on mhoran_psprep's response. This is the most important factor to consider in the points vs. rate question. With a horizon that long it sounds like the points are probably a better option for you.

There is a neat comparison tool at The Mortgage Professor's website that may help you build your spreadsheet or simply check the numbers you are getting.

Using the fact that you'd save \$160/mo by spending \$7000, I'd look at it this way -

If I were to lend you the \$7000 at 12%/yr, \$160 would pay it off in 58 months. At 18%/yr, 72 months or just 6 years. You can run spreadsheets to get breakeven scenarios, and mhoran is on track with his answer, but breakeven is just one point to consider. Beyond that date, it's free money.

My approach is to look at it with a question - "How much interest could I afford to pay to make that monthly savings worthwhile?"