Mortgage Points Calculator Formula

Understand the math behind the mortgage points calculator. Each variable explained with a worked example.

Formulas Used

Cost of Points

cost_of_points = points_cost

Monthly Payment Savings

monthly_payment_savings = monthly_savings

Break-Even Period (months)

breakeven_months = monthly_savings > 0 ? points_cost / monthly_savings : 0

Lifetime Savings

lifetime_savings = monthly_savings * n - points_cost

Monthly Payment (no points)

payment_no_points = pmt_base

Monthly Payment (with points)

payment_with_points = pmt_reduced

Variables

VariableDescriptionDefault
loan_amountLoan Amount(USD)300000
base_rateBase Interest Rate (no points)(%)7
reduced_rateReduced Rate (with points)(%)6.5
pointsDiscount Points1.5
loan_term_yearsLoan Term(years)30
points_costDerived value= loan_amount * points / 100calculated
r_baseDerived value= base_rate / 100 / 12calculated
r_reducedDerived value= reduced_rate / 100 / 12calculated
nDerived value= loan_term_years * 12calculated
pmt_baseDerived value= r_base > 0 ? loan_amount * r_base * pow(1 + r_base, n) / (pow(1 + r_base, n) - 1) : loan_amount / ncalculated
pmt_reducedDerived value= r_reduced > 0 ? loan_amount * r_reduced * pow(1 + r_reduced, n) / (pow(1 + r_reduced, n) - 1) : loan_amount / ncalculated
monthly_savingsDerived value= pmt_base - pmt_reducedcalculated

How It Works

Mortgage Points Explained

Discount points are upfront fees paid to the lender at closing in exchange for a lower interest rate. One point equals 1% of the loan amount.

How It Works

1. You pay a lump sum upfront (cost of points) 2. Your interest rate is permanently reduced 3. Your monthly payment decreases 4. Over time, the cumulative savings exceed the upfront cost

Break-Even Analysis

Break-Even Months = Cost of Points / Monthly Savings

If you plan to keep the mortgage longer than the break-even period, buying points saves money. If you might sell or refinance sooner, skip the points.

Worked Example

A $300,000 loan at 7% for 30 years. Paying 1.5 points to reduce the rate to 6.5%.

loan_amount = 300000base_rate = 7reduced_rate = 6.5points = 1.5loan_term_years = 30
  1. 01Cost of points: $300,000 x 1.5% = $4,500
  2. 02Monthly payment at 7%: $1,995.91
  3. 03Monthly payment at 6.5%: $1,896.20
  4. 04Monthly savings: $1,995.91 - $1,896.20 = $99.71
  5. 05Break-even: $4,500 / $99.71 = 45 months (about 3.8 years)
  6. 06Lifetime savings: $99.71 x 360 - $4,500 = $31,396

Ready to run the numbers?

Open Mortgage Points Calculator