Image source: Images Money.

Banks offer potential mortgage borrowers the opportunity to "buy points" on mortgage loans to lower the interest rate. Is it a smart move for first-time homebuyers?

The answer, of course, is that it depends. Let's break down the decision-making process.

A few assumptions
When it comes to mortgage loans, there really isn't any one-size-fits-all solution. That holds true in the world of discount points as well.

A borrower with a huge down payment, an amazing credit score, and boatloads of cash flow will probably find better deals than another borrower with a higher risk profile.

That said, we can use the following parameters to demonstrate the decision-making process while keeping the example relatively simple at the same time:

• One discount point generally costs 1% of the total loan amount.
• One discount point lowers the interest rate by 0.125% to 0.25%.
• We will assume the borrower is applying for a fixed-rate mortgage, meaning the interest rate and payment will never change throughout the life of the loan.

With those parameters established, let's dive into a case study. In this case, we'll be borrowing \$100,000 at a 5% interest rate with a 30-year loan term. (Who doesn't love working with nice, round numbers?)

The bank has offered us the opportunity to pay 1% per discount point and lower our interest rate by 0.125% per point purchased.

Here is a chart breaking down buying no points and buying one point. This chart was created using this mortgage calculator to break down the interest paid with the two different interest rates on a yearly basis.

Loan A: 5% With No PointsLoan B: 4.875% After 1 PointBreak-even Calculation
Yearly Cost Cumulative Cost Yearly Cost Cumulative Cost
Cost of Points  \$ --    \$1,000.00
Year 1  \$4,966.49  \$4,966.49  \$4,841.58  \$5,841.58  (\$875.09)
Year 2  \$4,891.01  \$9,857.50  \$4,766.36  \$10,607.94  (\$750.44)
Year 3  \$4,811.67  \$14,669.17  \$4,687.38  \$15,295.32  (\$626.15)
Year 4  \$4,728.26  \$19,397.43  \$4,604.47  \$19,899.79  (\$502.36)
Year 5  \$4,640.59  \$24,038.02  \$4,517.42  \$24,417.21  (\$379.19)
Year 6  \$4,548.44  \$28,586.46  \$4,426.03  \$28,843.24  (\$256.78)
Year 7  \$4,451.57  \$33,038.03  \$4,330.09  \$33,173.33  (\$135.30)
Year 8  \$4,349.74  \$37,387.77  \$4,229.36  \$37,402.69  (\$14.92)
Year 9  \$4,242.70  \$41,630.47  \$4,123.62  \$41,526.31  \$104.16
Year 10  \$4,130.19  \$45,760.66  \$4,012.60  \$45,538.91  \$221.75

Looking at the "Breakeven Calculation" column, we can see that buying the discount points today will begin saving money, in aggregate, in year nine.

Therefore, buying one point for \$1,000 to lower the interest rate by 0.125% will only save money if we keep the mortgage for nine years or longer.

The savings pile up quickly if you maintain that same mortgage past nine years, but as a first-time homebuyer it's very, very difficult to see a decade into the future.

If we sell the house or refinance the loan anytime before that, buying the points actually loses us money.

It should come as no surprise that the breakeven point is so far into the future.

Bank's are smart enough to know that most borrowers won't keep their mortgage for the full 30-year period, and they design these offers to favor the bank in the long run.

You can think about it kind of like designing a casino game -- the player may be able to win on occasion, but over the long haul the casino has the better odds and will ultimately win.

Image source: Images Money.

Remember those assumptions?
At the beginning of this example, we made the assumption that one discount point would cost us 1% of the loan amount and lower the interest rate 0.125%. Those assumptions are the levers that will determine whether buying discount points is right for you.

For example, if the cost was 0.5% of the loan amount (\$500, in this example) and everything else remained the same, buying the point would break even in year five. That's a huge change and would almost certainly change your decision.

The key in your own journey to homeownership is to do the work to find the breakeven for your specific situation.

Use a mortgage calculator like the one I've linked to and calculate the interest you'll pay each year. Write out your own table and find that breakeven year. Then you have to make your best assumption as to how long you'll keep your mortgage. The decision from there is purely dollars and cents.

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