Loan Repayment Schedule: Calculate Monthly Payments

A loan repayment schedule shows how each payment is divided between interest and principal, and how the balance changes over time. Enter the loan amount, annual APR, and term to calculate the level monthly payment and total interest under a fixed-rate, monthly-payment model.

Formula

For a fixed-rate loan with equal monthly payments, the payment is calculated as:

M = round(P × r / (1 − (1 + r)−n), 2)

• M is the monthly payment in dollars.
• P is the starting loan principal in dollars.
• r is the monthly interest rate, calculated as APR ÷ 1,200. APR is entered as a percentage per year.
• n is the number of monthly payments, calculated as the term in years × 12.

The calculator then estimates total interest as M × n − P. Because the payment is rounded to cents first, this total uses the rounded monthly payment, as real payment amounts are generally stated in currency units. The calculation assumes the scheduled payment is made for every month and does not model a final adjusted payment.

Worked Example

Using the calculator’s default values—$20,000 principal, 8% APR, and a five-year term:

1. Convert the annual APR to a monthly decimal rate: r = 8 ÷ 1,200 = 0.0066667.
2. Calculate the number of payments: n = 5 × 12 = 60.
3. Substitute the values: M = 20,000 × 0.0066667 ÷ (1 − (1 + 0.0066667)−60).
4. The monthly payment rounds to $405.53.
5. Multiply that rounded payment by 60: $405.53 × 60 = $24,331.80 in scheduled payments.
6. Subtract the original principal: $24,331.80 − $20,000 = $4,331.80 estimated total interest.

Assumptions

• The interest rate stays fixed for the full term.
• Payments are equal, made monthly, and applied at the end of each monthly period.
• Interest compounds monthly using APR divided by 12.
• Fees, taxes, insurance, PMI, escrow, and other charges are not included.

How a Repayment Schedule Works

A repayment schedule, also called an amortization schedule, lays out the payment-by-payment path from the original balance to zero. For each period, interest is calculated on the outstanding balance. The remainder of the payment reduces principal. Since the balance generally declines over time, the interest portion usually falls and the principal portion usually rises when the payment and rate remain unchanged.

For example, in the first month of the worked example, estimated interest is $20,000 × 0.0066667, or about $133.33. Of the $405.53 payment, about $272.20 therefore goes toward principal. The next month’s interest is calculated on the smaller remaining balance, not on the original $20,000. Small differences can arise when a lender uses daily interest, different payment dates, or its own rounding conventions.

The calculator gives the regular payment and total interest, rather than displaying every row of the schedule. To construct a full schedule, repeat the same process for each month: calculate interest on the starting balance, subtract it from the payment to find principal repaid, then subtract that principal from the balance.

When to Use the Estimate and How to Read It

This calculation is useful for understanding the basic payment mechanics of an installment loan or checking how principal, APR, and term relate mathematically. The inputs should match the figures in the lender’s loan disclosure: use the amount actually financed as principal, the stated annual APR, and the repayment term. If a quoted rate or term differs from the final agreement, the calculated schedule will differ too.

A longer term spreads repayment over more months and, with the same principal and rate, generally lowers the scheduled monthly payment while increasing total interest. A higher rate generally increases both the payment and interest cost for a fixed term. These are arithmetic effects, not a judgment about whether a particular loan or payment arrangement is suitable for anyone.

The total-interest figure is not the same as the sum of all borrowing-related costs. It is derived from the rounded payment and principal only. To understand the full amount due, review the lender’s itemized disclosures for applicable charges and payment terms. For a true repayment schedule, request or generate a table that includes the dates, payment allocation, and remaining balance for each period.

Common Calculation Errors and Limits

• Using APR as a whole number in the wrong place: An 8% annual rate becomes 0.08 per year, then 0.08 ÷ 12 per month. In this calculator, apr / 1200 performs both conversions.
• Mixing years and months: The term is entered in years, so the number of payments is years × 12. If a loan document gives a term in months, convert it before entering it.
• Rounding too early: Rounding the monthly rate or intermediate values can slightly change the result. The formula keeps the rate calculation unrounded and rounds the payment to cents.
• Assuming every loan is level-payment: Variable-rate loans, interest-only periods, balloon payments, irregular payment dates, and payment holidays do not follow this simple schedule throughout their lives.
• Confusing APR with every amount charged: This calculation uses APR as the interest-rate input but does not separately model fees or other charges. The lender’s disclosure is needed for contract-specific figures.

An APR of 0% is outside this calculator’s input range because the stated payment formula divides by the monthly rate. A zero-interest loan can instead be calculated by dividing principal by the number of payments, subject to the actual agreement’s rounding and payment terms.

Frequently Asked Questions

How do I calculate a monthly loan payment?
Convert APR to a monthly decimal rate by dividing the percentage by 1,200, convert the term to months, and apply the fixed-payment formula shown above. Round the resulting payment to the nearest cent.

How do I calculate total interest on a loan?
For this fixed-payment estimate, multiply the rounded monthly payment by the number of payments, then subtract the original principal. The result excludes charges that are not part of the model.

Why does the interest portion decrease over time?
Each period’s interest is based on the outstanding principal. As payments reduce that balance, less interest accrues at the same rate, leaving more of the level payment to repay principal.

Does this schedule include fees or insurance?
No. It models principal and interest under the stated assumptions, not fees, taxes, insurance, PMI, or escrow. Check the loan disclosure for any additional amounts.

Will my lender’s payment match this estimate exactly?
Not necessarily. Payment dates, daily-interest methods, rounding, fees, rate changes, or contract-specific payment rules can affect the figures. The result is an estimate, and the lender’s disclosure gives the exact figures.

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in p | Loan amount | $ | 20000 | 1 | 100000000
in apr | Interest rate (APR) | % | 8 | 0.01 | 100
in yrs | Loan term | years | 5 | 0.0833 | 50
out pmt | Monthly payment | $ | round(p * (apr / 1200) / (1 - (1 + apr / 1200) ^ -(yrs * 12)), 2) | 2
out int | Total interest | $ | pmt * yrs * 12 - p | 2