Payment Calculator

Use this payment calculator to find your payment for a fixed-rate loan and see totals like total interest and total paid. You can also switch payment frequency and add an extra payment to estimate how much faster you could pay the loan off.

How to use our Payment Calculator

1. Choose Solve for: Payment (most common), Loan amount (max you can borrow), or Term (how long it takes).
2. Pick a Payment frequency (monthly, biweekly, weekly, etc.). This sets how many payments happen per year.
3. Enter the Annual interest rate (APR %) as a percent (example: 6.5, not 0.065).
4. Enter the Loan term and choose the Term unit (years or months).
5. If Solve for uses it, enter either Loan amount (USD) or Target payment per period (USD).
6. Open Advanced options to add an Extra payment each period or Financed upfront fees (fees get added to the starting balance).
7. Click Calculate.
8. Read the results: payment per period, total interest, and (if extra payment is used) the estimated faster payoff time and interest saved.

Definitions

Principal: The amount you borrow (your starting balance).

APR (annual percentage rate): A yearly rate shown as a percent. It is used here as the loan’s annual rate and is converted to a per-payment-period rate. APR can be different from the simple interest rate because it may reflect some costs too [2][3].

Term: How long you take to pay back the loan (for example, 5 years).

Payment frequency: How often you pay (monthly, biweekly, weekly). This controls how many payments happen per year.

Amortization: Paying a loan down over time with regular payments, where each payment covers interest first and then reduces the balance [1].

Methodology

Inputs used in the math

The starting balance is: loan amount + financed upfront fees.

The calculator assumes a fixed APR for the whole loan and a fixed payment each period (unless you add an extra payment).

1) Payments per year

ppy = {12 monthly, 26 biweekly, 52 weekly, 24 semimonthly, 4 quarterly, 1 yearly}

2) Convert term to number of payments

n = (term_years * ppy) OR n = (term_months / 12) * ppy

If n is not greater than 0, the calculator shows an error.

3) Convert APR to a periodic interest rate

r = (apr_percent / 100) / ppy

This treats APR as a nominal annual rate divided by payments per year. APR is commonly presented as a yearly percent [2].

4) Solve for payment (fixed-rate amortizing loan)

payment = balance * r / (1 - (1 + r)^(-n))

if r = 0, then payment = balance / n

This is the standard amortized-loan payment relationship, where payments are designed to bring the balance down to 0 over n payments [1].

5) Totals without extra payments

total_paid_no_extra = payment * n

total_interest_no_extra = total_paid_no_extra - balance

6) Interest-only payment (comparison)

interest_only_payment = balance * r

This is only a comparison. Paying only interest would not reduce the balance.

7) Extra payment payoff simulation

If extra payment is greater than 0, the calculator simulates payments period-by-period until the balance reaches 0 (or a tiny near-zero threshold for cents rounding). Each step uses:

interest_t = balance_t * r

principal_t = min(balance_t, (payment + extra) - interest_t)

balance_(t+1) = balance_t - principal_t

If (payment + extra) is less than or equal to interest_t at any step, the balance will not go down (negative amortization). In that case, payoff time and interest saved show as N/A with an explanation.

The last payment is reduced if needed so the balance ends at exactly 0, which avoids overpaying in the totals.

8) Solve for loan amount (given a target payment)

When Solve for is Loan amount, the calculator rearranges the payment formula to get the maximum starting balance that fits the target payment:

if r = 0: max_balance = target_payment * n

if r > 0: max_balance = target_payment * (1 - (1 + r)^(-n)) / r

The output includes financed upfront fees because they are part of the starting balance.

9) Solve for term (given a target payment)

When Solve for is Term, the calculator finds the term that makes the payment less than or equal to the target payment.

If r = 0, term is straightforward:

n_required = balance / target_payment

If r > 0, the calculator uses the closed-form solution for the number of payments:

n_required = -ln(1 - (balance * r / target_payment)) / ln(1 + r)

If target_payment is less than or equal to balance * r, the payment does not even cover the first period’s interest, so the loan can never be paid off. The required term shows as N/A with that reason.

The calculator then converts payments to years:

required_term_years = n_required / ppy

Sources