Loan Amortization: Payment, Interest and Balance

Set up one consistent repayment model

An amortization schedule follows the balance after each payment and separates interest from principal. For a fixed monthly payment model, identify principal P, monthly rate i, payment count n and end-of-month timing. If the stated annual nominal rate is 12%, then i=0.12/12=0.01. A two-year monthly loan has n=24. The formula assumes equal payment intervals and an unchanged rate; it does not automatically describe daily-interest accounts, interest-only periods, extra repayments or a final balloon. Start with a clearly labeled model before building rows that otherwise look authoritative.

Calculate the fixed payment

For a nonzero monthly rate, M=P×i/[1−(1+i)^(-n)]. With P=12000, i=0.01 and n=24, M is approximately 564.881666679, displayed as 564.88. For a zero rate, use M=P/n instead of dividing by an expression that becomes zero. Microsoft documents Excel's PMT as a constant-rate, constant-payment function; =PMT(12%/12,24,-12000,0,0) returns the positive payment for this example. The negative principal follows the cash-flow sign convention, and the last zero selects end-of-period payments. Those period units and timing must agree with the schedule you construct.

Build the first row from the opening balance

Let B0=12000 be the balance before any payment. Month-one interest is I1=B0×i=120. Principal repaid is Q1=M−I1, approximately 444.881666679. The closing balance is B1=B0−Q1, approximately 11555.118333321. Displaying cents gives interest 120.00, principal 444.88 and balance 11555.12. The interest and principal portions together equal the installment before rounding. Notice that the first row does not subtract the entire 564.88 from principal: doing so would erase the interest charge and make every later balance too low.

Carry the closing balance into the next row

For month two, use B1 as the new opening balance. Interest is approximately 115.551183333, principal repaid approximately 449.330483346, and the closing balance approximately 11105.787849975. Rounded for display, those are 115.55, 449.33 and 11105.79. Repeat the same recurrence for each period: interest equals opening balance times monthly rate, principal equals payment minus interest, and closing balance equals opening balance minus principal. The fixed payment stays constant while the interest portion falls and the principal portion rises under this particular model.

Check an intermediate and the final balance

After twelve payments, the unrounded recurrence gives a balance of about 6357.786921825, displayed as 6357.79. This is more than half the original principal even though half the payments have occurred, because early installments allocate more to interest. After all 24 payments, the balance should be essentially zero apart from numerical rounding. Total principal repaid should equal 12000, total payments should be about 13557.16 and interest about 1557.16. These independent totals help expose a shifted row reference, a missing payment or an annual rate accidentally applied every month.

Reproduce the local tool's actual display

Enter principal 12000, annual rate 12 and tenure 2 years in the Loan Amortization Calculator. It reports the full-term payment and interest totals, but displays only the first twelve monthly rows when the loan is longer. Its remaining-months note is not a downloadable complete schedule. Use the recurrence above or a spreadsheet to inspect later rows. Keep full precision internally and format displayed cells to two decimals when checking this model; rounding the balance after every step follows a different convention and can move the final installment by a small amount.

Adapt the schedule only when the contract supports it

An extra principal payment changes the next opening balance, but its effect on the required installment or payoff date depends on the agreement. A changed rate requires a documented reset rule. Fees financed into principal belong in the opening balance, while charges paid separately need their own cash-flow entries. Do not add them to total interest without identifying what that total represents. Compare the model with the lender's dated statement, payment allocation and final payoff instructions. An amortization table is a transparent record of assumptions; it is not evidence that an actual contract uses those assumptions or permits a payment change.

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