Loan Amortization Calculator: Annual Payment Schedule

A loan amortization calculator estimates the fixed monthly payment and total interest for a fixed-rate loan from its amount, APR, and term. The schedule below is annual rather than month by month: it summarizes how much of each year’s payments goes to interest and principal, and what balance remains.

Formula

The calculator uses the standard fixed-payment loan formula. Let P be the starting principal in dollars, a the annual percentage rate (APR) in percent, r = a / 1200 the monthly interest rate as a decimal, and n = 12 × years the number of monthly payments. The monthly payment is M = P × r / [1 − (1 + r)⁻ⁿ]. Total interest over the full term is I = M × n − P. The payment is rounded to cents before total interest is calculated.

An annual schedule is produced by grouping the monthly amortization calculations into calendar-like loan years. For each month, interest is the prior balance multiplied by r; principal repaid is the monthly payment minus that interest; and the new balance is the prior balance minus principal repaid. For each year, add that year’s 12 monthly interest amounts and principal amounts. The final year may contain fewer than 12 payments if a loan is paid off early or has an irregular term.

Worked Example

Using the calculator’s default inputs: principal P = $20,000, APR a = 8%, and term of 5 years:

1. Monthly rate: r = 8 / 1200 = 0.0066667.
2. Number of payments: n = 5 × 12 = 60.
3. Monthly payment: M = 20,000 × 0.0066667 / [1 − (1.0066667)⁻⁶⁰] = $405.53, rounded to cents.
4. Total of scheduled payments: $405.53 × 60 = $24,331.80.
5. Total interest: $24,331.80 − $20,000 = $4,331.80.

For an illustrative first-year schedule, applying the monthly calculation repeatedly gives approximately $1,495.83 in principal reduction and $3,370.53 in interest. The balance after 12 payments is about $18,504.17. Annual figures are rounded here for display; calculations should retain precision internally and round displayed money to cents. Small differences in a published lender schedule can arise from payment dates, day-count conventions, or a final-payment adjustment.

Assumptions

• The interest rate is fixed for the entire modeled term.
• Payments are equal monthly payments made at the end of each monthly period.
• Interest accrues monthly at APR divided by 12; this is the calculator’s simplifying convention.
• The model excludes fees, taxes, insurance, PMI, escrow, and any charges not entered as part of the loan amount.
• It assumes payments arrive as scheduled, with no extra payments, missed payments, rate changes, or payment-date adjustments.

How to Read an Annual Amortization Schedule

A typical schedule has one row for each loan year and columns for beginning balance, payments made, principal repaid, interest paid, and ending balance. The beginning balance for a year should match the preceding year’s ending balance. Principal plus interest should equal the scheduled payments for that period, subject to rounding and any final-payment adjustment.

Early in a fully amortizing loan, the balance is relatively high, so a larger share of each payment generally goes to interest. As principal falls, the interest charged each month falls too, and more of the fixed payment reduces principal. This does not mean the lender changes the payment allocation arbitrarily; it follows from applying the interest rate to the balance that remains.

The calculator’s total-interest output describes the full scheduled term, not the interest for the first year. To make an annual schedule, a lender statement, spreadsheet, or a calculator with a schedule table is needed to show each year’s split. The two outputs here provide the payment and overall interest totals from which that schedule can be checked.

When to Use It and What It Does Not Show

Use an amortization estimate to understand how a stated principal, APR, and term translate into a level payment, how the balance declines over time, and how total interest relates to the amount borrowed. It can also help you check arithmetic in a quote, provided the quote uses the same assumptions. Enter the actual proposed loan amount, annual APR, and term supplied in the lender’s disclosure; the 8% example is only a neutral illustration, not a claim about available rates.

This is not necessarily the same as a complete monthly bill. A mortgage payment, for example, may include escrowed items or other charges; this calculator does not estimate them. An APR may include certain borrowing costs in its disclosed calculation, but this simple formula treats the entered APR as a monthly rate and does not separately model fees or the timing of those costs. Variable-rate loans, interest-only periods, balloon payments, and loans with irregular payment schedules require a different model or additional inputs.

Common Schedule Errors and Rounding

• Confusing APR with a monthly rate: enter the annual percentage as a percent, such as 8, not 0.08 and not 8 as a monthly rate. The formula converts it to a monthly decimal by dividing by 1,200.
• Using years as months: the term field is in years; the formula multiplies it by 12. A five-year term means 60 monthly payments.
• Rounding each month too early: rounding interest and balance at every step can create small differences across a long schedule. Retain full precision during calculations and round displayed amounts to cents.
• Assuming the final payment is always identical: rounding, payment dates, or a lender’s accrual method may make the last payment slightly different from the modeled payment.

Extra principal payments can shorten repayment and reduce interest, but they are not included in this fixed-payment estimate. Their effect depends on when they are made and how the servicer applies them. A schedule with extra payments needs those amounts and dates as inputs; simply subtracting an extra payment from total interest would not produce a reliable result.

Frequently Asked Questions

What does an annual loan amortization schedule show?
It groups the loan’s monthly payments by year and reports how much went to principal and interest, along with the remaining balance at year-end. Annual totals are sums of the monthly calculations.

How do I calculate the monthly payment from an annual interest rate?
Convert the APR to a monthly decimal by dividing by 1,200, convert the term to months, and use the fixed-payment formula shown above. The result assumes the same rate and payment throughout the term.

Why does the interest portion decline over time?
Monthly interest is calculated on the unpaid balance. As scheduled payments reduce that balance, less interest accrues in later periods, leaving more of each level payment to reduce principal.

Does total interest include fees or insurance?
No. The total-interest figure is calculated from the modeled payment and principal. Fees, insurance, taxes, escrow, and other charges are not separately included.

Will my lender’s schedule match this estimate exactly?
Not always. Payment dates, rounding, fee treatment, daily interest methods, and final-payment adjustments can affect the lender’s figures. Compare the assumptions and use the lender’s disclosure for the exact schedule.

This result is an estimate, and the lender’s disclosure gives the exact figures.

Related

• Simple Interest Loan Calculator: I = P × r × t
• Interest-Only Loan Calculator: Payment During and After the Interest-Only Period
• APR Calculator: The True Rate of a Loan With Fees

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 | $ | p * (apr / 1200) / (1 - (1 + apr / 1200) ^ -(yrs * 12)) | 2
out int | Total interest | $ | pmt * yrs * 12 - p | 2