Hong Life CalculatorsUnderstanding the loan payoff amount calculator — concept and principle
If you want to repay a car loan, personal loan or mortgage early, the amount needed is not the balance on your last statement. Interest has built up since the last payment, and some loans charge a prepayment penalty. This calculator estimates the payoff amount today on an equal-payment loan, splits it into principal, accrued interest and penalty, and shows how much interest you avoid compared with making every remaining payment.
How it is calculated
With loan amount P, monthly rate i = annual rate ÷ 12, total payments n, payments made k and days since the last payment d:
- Monthly payment a = P × i ÷ (1 − (1 + i)^(−n))
- Principal balance B = P × (1 + i)^k − a × ((1 + i)^k − 1) ÷ i
- Accrued interest = B × annual rate ÷ 365 × d
- Penalty = B × penalty %
- Payoff amount = B + accrued interest + penalty
- Remaining payments = a × (n − k)
- Interest avoided = remaining payments − B − accrued interest − penalty
The principle
On an amortizing loan, each payment covers the month's interest on the balance and the rest reduces the principal. The balance formula grows the original amount with interest for k months and subtracts the payments made, also with interest. Between payments, interest keeps accruing day by day, here at the annual rate divided by 365, so the payoff is slightly higher than the balance. Paying off early saves the interest that the future payments would have contained.
Worked example
- Loan $25,000, 7.5% a year, 5 years (60 payments), 20 paid, 12 days since the last payment, no penalty.
- Monthly payment = 25,000 × 0.00625 ÷ (1 − 1.00625^(−60)) ≈ $500.95.
- Balance after 20 payments ≈ $17,680.93.
- Accrued interest = 17,680.93 × 0.075 ÷ 365 × 12 ≈ $43.60.
- Payoff = 17,680.93 + 43.60 + 0 = $17,724.53.
- Remaining 40 payments ≈ $20,037.95; interest avoided = 20,037.95 − 17,680.93 − 43.60 ≈ $2,313.42.
How to read the result
The interest avoided is the saving from paying off now rather than keeping the loan to the end. It is largest early in the loan, when most of each payment is interest, and shrinks as the end approaches. Compare it with what the same money could do elsewhere and with any penalty; a penalty can wipe out much of the saving late in the term.
Common mistakes
- Paying the statement balance and leaving a small unpaid amount of accrued interest.
- Assuming every lender uses a 365-day year; some use 360 days or other methods.
Frequently asked questions
Why is the payoff amount higher than my balance?
Interest accrues every day after the last payment, and that interest must be paid too.
How much do I save by paying off a loan early?
Roughly the interest left in the remaining payments, minus accrued interest and any penalty; here about $2,313.
Do all loans charge prepayment penalties?
No; it depends on the contract and local law, so check the loan agreement.
Sources: Standard time value of money mathematics (loan balance after k payments) · U.S. Consumer Financial Protection Bureau, "What is a payoff amount?"