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_costMonthly Payment Savings
monthly_payment_savings = monthly_savingsBreak-Even Period (months)
breakeven_months = monthly_savings > 0 ? points_cost / monthly_savings : 0Lifetime Savings
lifetime_savings = monthly_savings * n - points_costMonthly Payment (no points)
payment_no_points = pmt_baseMonthly Payment (with points)
payment_with_points = pmt_reducedVariables
| Variable | Description | Default |
|---|---|---|
loan_amount | Loan Amount(USD) | 300000 |
base_rate | Base Interest Rate (no points)(%) | 7 |
reduced_rate | Reduced Rate (with points)(%) | 6.5 |
points | Discount Points | 1.5 |
loan_term_years | Loan Term(years) | 30 |
points_cost | Derived value= loan_amount * points / 100 | calculated |
r_base | Derived value= base_rate / 100 / 12 | calculated |
r_reduced | Derived value= reduced_rate / 100 / 12 | calculated |
n | Derived value= loan_term_years * 12 | calculated |
pmt_base | Derived value= r_base > 0 ? loan_amount * r_base * pow(1 + r_base, n) / (pow(1 + r_base, n) - 1) : loan_amount / n | calculated |
pmt_reduced | Derived value= r_reduced > 0 ? loan_amount * r_reduced * pow(1 + r_reduced, n) / (pow(1 + r_reduced, n) - 1) : loan_amount / n | calculated |
monthly_savings | Derived value= pmt_base - pmt_reduced | calculated |
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%.
- 01Cost of points: $300,000 x 1.5% = $4,500
- 02Monthly payment at 7%: $1,995.91
- 03Monthly payment at 6.5%: $1,896.20
- 04Monthly savings: $1,995.91 - $1,896.20 = $99.71
- 05Break-even: $4,500 / $99.71 = 45 months (about 3.8 years)
- 06Lifetime savings: $99.71 x 360 - $4,500 = $31,396
Ready to run the numbers?
Open Mortgage Points Calculator