Straight Line Loan Amortization: Formula and Calculator

Straight-line loan amortization repays the same amount of principal in every payment, while interest generally declines as the balance falls. This calculator estimates the fixed monthly principal payment and total interest for a loan with a fixed annual rate; enter the amount, APR, and term to see those results.

Formula

In straight-line amortization, the principal portion is divided evenly across the loan term. The calculator treats the term as a whole number of monthly periods and assumes interest for each period is calculated on the balance at the start of that period.

• Monthly principal: P ÷ n
• Monthly interest in period k: (P − (k − 1) × P ÷ n) × r
• Payment in period k: P ÷ n + monthly interest in period k
• Total interest: P × r × (n + 1) ÷ 2

Here, P is the original principal in dollars, n is the number of monthly payments (term in years × 12), r is the monthly interest rate as a decimal (APR ÷ 1,200), and k is a payment number from 1 through n. The calculator’s first output, “Monthly payment,” is the first payment: later payments decrease because interest is charged on a progressively smaller balance. The interest output is the sum across all periods.

Worked Example

Using the defaults: P = $20,000, APR = 8%, and a five-year term.

1. Convert the term to monthly periods: n = 5 × 12 = 60.
2. Convert APR to a monthly decimal rate: r = 8 ÷ 1,200 = 0.0066667.
3. Find monthly principal: $20,000 ÷ 60 = $333.3333…
4. Find first-month interest: $20,000 × 0.0066667 = $133.3333…
5. Add principal and first-period interest: $333.3333… + $133.3333… = $466.67 rounded to cents.
6. Find total interest: $20,000 × 0.0066667 × 61 ÷ 2 = $4,066.67 rounded to cents.

So the calculator displays a first monthly payment of $466.67 and estimated total interest of $4,066.67. The final payment can differ slightly from the calculated pattern in an actual repayment schedule because lenders may round each installment to cents and adjust the last amount.

Assumptions

• The interest rate stays fixed for the full term.
• Payments are monthly, made at the end of each period; the first payment includes a full period of interest.
• Interest is calculated monthly using APR divided by 12 (APR ÷ 1,200 as a decimal).
• The calculation excludes fees, taxes, insurance, PMI, escrow, late charges, and any extra or missed payments.

How Straight-Line Amortization Works

“Straight-line” describes the principal repayment, not a constant total payment. Every installment reduces the original principal by the same amount. Since interest is calculated on the remaining balance, the interest charge falls each month, and the total payment falls by the same amount from one period to the next, before rounding.

For the example, principal repayment is about $333.33 per month. The first payment includes about $133.33 of interest. After the first installment, the balance is approximately $19,666.67; the next month’s interest is about $131.11, making the next payment about $464.44. This pattern continues until the balance is repaid.

The interest formula follows from adding the balances that accrue interest: P, then P − P/n, then P − 2P/n, and so on, down to P/n before the final payment. Those n balances form an arithmetic sequence with an average of P(n + 1)/(2n). Multiplying their sum by the monthly rate gives total interest P × r × (n + 1)/2.

When to Use This Estimate

This calculation is useful when a loan contract or a quoted repayment method explicitly uses equal principal installments, or when you want to understand how declining-balance interest behaves under that structure. It provides a first-payment estimate and a total-interest estimate from the entered amount, rate, and term.

It is not a standard level-payment amortization calculator. Many familiar installment-loan examples use equal total payments: the payment stays level, while the principal share grows over time and the interest share shrinks. With straight-line principal, the principal share stays level and the total payment declines. Confirm which schedule the lender’s documents specify before comparing a calculator result with a quoted payment.

Reading the Results and Common Errors

• Do not treat the first payment as every payment. The displayed monthly payment is the first installment; subsequent payments are lower under the assumptions above.
• Check the rate conversion. An APR entered as 8 means 8 percent per year, converted here to 8 ÷ 1,200 per month—not 8 as a decimal monthly rate.
• Check the term units. The input is in years and is multiplied by 12. A five-year loan therefore has 60 monthly periods.
• Separate principal from interest. The amount of principal repaid monthly is P/n; the total payment also includes that month’s interest.
• Expect rounding differences. The displayed estimates are rounded to cents. A lender’s schedule can use daily accrual, specific payment dates, fees, or other contract terms and may not match exactly.

How It Differs from Level-Payment Amortization

In level-payment amortization, the total scheduled payment is constant when the rate and payment interval are fixed. Early payments usually allocate more to interest and less to principal; later payments do the opposite. In straight-line amortization, principal is equal each period, so total payments decline over time. The total interest also differs: it depends on the repayment pattern, not just the loan amount and APR.

Neither label by itself tells you the full cost of borrowing. The schedule does not include fees or other charges unless they are included in the stated principal or modeled separately. To compare figures, use the actual rate, term, repayment method, timing, and charges shown in the lender’s disclosure.

Frequently Asked Questions

Is a straight-line loan payment the same every month?
No. The principal portion is the same, but interest declines as the balance is repaid, so the total scheduled payment usually decreases each month.

How do I calculate straight-line loan amortization?
Divide the original principal by the number of payments to get equal principal installments. For each period, calculate interest on the balance at the start of that period, then add that interest to the principal installment.

Does straight-line amortization mean simple interest?
Not necessarily. “Straight-line” refers to equal principal installments. This calculator applies periodic interest to the outstanding balance; a contract’s use of the term and its interest method should be checked in its documents.

Why is my lender’s payment different?
The schedule may use a different repayment method, payment dates, daily rather than monthly accrual, fees, or rounding rules. Compare the calculator’s assumptions with the lender’s stated schedule.

Can I use this calculator for a mortgage or car loan?
Only if the loan’s repayment schedule is equal-principal, straight-line amortization and the stated assumptions fit. Many loans instead use level total payments, so this result may not represent their payment schedule.

This result is an estimate; 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 | $ | p / (yrs * 12) + p * (apr / 1200) | 2
out int | Total interest | $ | (p * (apr / 1200)) * ((yrs * 12) + 1) / 2 | 2