Loan Repayment Calculator

Estimate a monthly payment for a chosen loan term, or find payoff time for a payment you choose. The schedule includes interest and extras. Cent rounding can leave a small balance for an additional final payment.

How to use our Loan Repayment Calculator

1. Choose what you want to solve for: "Monthly payment" (you pick months) or "Payoff time" (you pick payment).
2. Enter your loan balance in dollars (the amount you owe or plan to borrow).
3. Enter the interest rate as APR percent (for example, 6.5 for 6.5%).
4. If you chose "Monthly payment" mode, enter the repayment time in months (like 60 for 5 years).
5. If you chose "Payoff time" mode, enter your monthly payment in dollars.
6. Open Advanced options if needed: pick the first payment month to get an estimated payoff month.
7. Still in Advanced options, add an origination fee percent, extra monthly payment, or a one-time extra payment (and its month) if you plan to pay extra.
8. Pick payment frequency (monthly or biweekly approximation) and rounding (cents is most realistic).
9. Click Calculate. If you see an error about the payment being too small, raise the payment, lower APR, or add time.

Definitions

Loan balance (principal): The amount you owe right now (or borrow). If you add an origination fee, this calculator treats it as added to what you owe.

APR (annual percentage rate): The yearly interest rate used to compute interest over time. A monthly rate is derived from APR for the schedule.

Interest: The cost of borrowing. Each period, interest is based on the current balance.

Payment: Money you send each period. It pays interest first, then the rest reduces the balance (principal) in the amortization breakdown. This is how amortized loans work. [4]

Amortization schedule: A month-by-month table showing how each payment is split between interest and principal, and how the balance changes. [4]

Negative amortization: When your payment is smaller than the interest for that period, so the balance grows instead of shrinking.

Prepayment: Paying extra (extra monthly or a lump sum) to reduce the balance faster. Some loans can charge prepayment penalties. [1]

Methodology

What this calculator solves

You can solve for (A) an estimated payment for a chosen term, or (B) the payoff time for a chosen payment. Cent rounding can add a small final payment in another month; the displayed payoff time and schedule show the actual result. It then builds an amortization schedule (period-by-period breakdown) and totals.

Step 1: Parse inputs and set the starting balance

If an origination fee percent is provided, the starting balance used for the schedule increases.

P0 = principal * (1 + orig_fee_percent/100)

If the origination fee is blank, then P0 = principal. (Real disclosures can separate amount financed and finance charge; this calculator uses a simple, common planning assumption.) [3]

Step 2: Convert APR to a periodic rate

For monthly compounding, convert APR to a monthly rate.

r = APR/100/12

If you select daily compounding, convert APR to an effective monthly rate (an estimate of one month worth of daily compounding).

r = (1 + (APR/100)/365)^(365/12) - 1

Step 3A: Monthly payment mode (solve for payment)

If you choose a repayment time of n months and a fixed rate r, the level payment that pays the balance to zero is:

PMT = P0 * r / (1 - (1 + r)^(-n))

If APR is 0 (so r = 0), avoid divide-by-zero and use:

PMT = P0 / n

Step 3B: Payoff time mode (solve for time)

If there are no extra payments and the payment is fixed, the payoff time can be estimated by the closed-form formula below. This is only valid when the payment is bigger than the first period interest.

n = -ln(1 - r*P0/PMT) / ln(1 + r)

If you use extra monthly payments, a lump sum, rounding, or biweekly approximation, the calculator finds payoff time by iterating the schedule month by month instead of relying on the closed-form formula.

Step 4: Payment frequency and biweekly approximation

If you choose "Biweekly (approx)", the calculator converts the entered monthly payment to an effective monthly amount using 26 half-payments per year. It then runs a monthly schedule using that effective monthly payment and adds a note that real biweekly timing can differ.

effective_monthly = (26 * (monthly_payment/2)) / 12

Step 5: Build the amortization schedule (the breakdown table)

Each period, interest is computed from the starting balance for that period. The regular payment is applied, then any extra payment for that period (extra monthly, plus a lump sum if the month matches).

interest_i = balance_{i-1} * r

principal_i = payment_i - interest_i

balance_i = balance_{i-1} - principal_i - extra_i

If the final period would overpay (balance would go below 0), the calculator reduces the last payment so the ending balance is exactly 0.00 when rounding to cents. (Many real loan statements and schedules show this same idea: small rounding differences can change the last payment.) [2]

Feasibility check (prevents misleading results)

If the total regular and extra payment in a period does not exceed that period's interest, this payoff model stops because the balance is not shrinking. In that case, the calculator stops and shows the minimum payment needed to keep the balance from growing at the start.

min_payment_to_stop_growth = P0 * r

Payoff month

If you enter a first payment month, the payoff month is the first month plus (number of schedule periods minus 1). If payoff is not feasible, no payoff month is shown.

Totals and ratios

Total paid is the sum of all regular payments plus all extra payments actually applied. Total interest is the sum of period interest. Total principal is total paid minus total interest. Interest as a share of total paid is total_interest divided by total_paid, shown as a percent.

Guards and edge cases

The schedule has a hard cap of 1200 months (100 years). If it would take longer, the calculator errors instead of looping forever. Lump sum month is required when a lump sum amount is entered; if the month is before the first payment month, it errors. If a lump sum is bigger than the remaining balance that month, the applied lump sum is capped to the remaining balance and a note is shown.

Sources