Extra Payment Calculator Formula

Understand the math behind the extra payment calculator. Each variable explained with a worked example.

Use the Extra Payment Calculator

Formulas Used

Months Saved

months_saved = n - new_n

Total Interest Saved

interest_saved = base_total_interest - new_total_interest

New Payoff Time (months)

new_payoff_months = new_n

Base Monthly Payment

base_pmt = base_payment

Total Monthly (with extra)

total_with_extra = total_payment

Original Total Interest

original_total_interest = base_total_interest

Variables

VariableDescriptionDefault
loan_amountOriginal Loan Amount(USD)300000
interest_rateInterest Rate(%)7
loan_term_yearsLoan Term(years)30
extra_monthlyExtra Monthly Payment(USD)300
rDerived value= interest_rate / 100 / 12calculated
nDerived value= loan_term_years * 12calculated
base_paymentDerived value= r > 0 ? loan_amount * r * pow(1 + r, n) / (pow(1 + r, n) - 1) : loan_amount / ncalculated
total_paymentDerived value= base_payment + extra_monthlycalculated
base_total_interestDerived value= base_payment * n - loan_amountcalculated
new_nDerived value= r > 0 ? log(total_payment / (total_payment - loan_amount * r)) / log(1 + r) : loan_amount / total_paymentcalculated
new_total_interestDerived value= total_payment * new_n - loan_amountcalculated

How It Works

Impact of Extra Mortgage Payments

Extra payments applied to principal reduce the balance faster, saving interest and shortening the loan term.

New Payoff Formula

New Months = log(PMT / (PMT - P x r)) / log(1 + r)

Where PMT is the total monthly payment (base + extra), P is the loan balance, and r is the monthly rate.

Why Extra Payments Are So Effective

  • Early in a mortgage, most of each payment goes to interest
  • Extra principal reduces the balance that accrues interest
  • The effect compounds: less interest means more of future payments go to principal
  • Even small extra amounts make a significant difference over decades

    • Strategies

  • Round up to the nearest hundred
  • Apply annual bonuses or tax refunds
  • Match extra payments to raises or eliminated expenses

    • Worked Example

    A $300,000 loan at 7% for 30 years with an extra $300/month.

    loan_amount = 300000interest_rate = 7loan_term_years = 30extra_monthly = 300
    1. 01Base payment: $1,995.91
    2. 02Total payment with extra: $1,995.91 + $300 = $2,295.91
    3. 03Original payoff: 360 months (30 years)
    4. 04New payoff: approximately 263 months (about 22 years)
    5. 05Months saved: 360 - 263 = 97 months (about 8 years)
    6. 06Original total interest: $418,528
    7. 07New total interest: approximately $303,726
    8. 08Interest saved: approximately $114,802

    Ready to run the numbers?

    Open Extra Payment Calculator