Negative Amortization Loan Calculator and Explanation

A negative amortization loan is a loan where a scheduled payment is too small to cover all the interest due, so the unpaid interest is added to the balance. This calculator estimates that growing balance from the starting loan amount, annual interest rate, payment amount, and number of months; it also shows the amount added through unpaid interest.

Formula

The calculator uses the standard fixed-rate balance formula, assuming monthly compounding and a payment made at the end of each month. The first output is the estimated balance after the selected number of months:

B_n = P(1 + r)ⁿ − M[((1 + r)ⁿ − 1) / r]

• B_n is the balance after n months, in dollars.
• P is the starting balance, in dollars.
• r is the monthly interest rate, calculated as APR ÷ 1,200.
• n is the number of monthly periods.
• M is the fixed monthly payment, in dollars.

The second output, balance increase, is B_n − P. A positive increase means the modeled balance grew; zero means it did not grow. The formula’s max(0, …) prevents a negative displayed balance if the entered payment would more than repay the loan. It does not model a final partial payment.

Worked Example

Using the calculator’s default inputs—$20,000 starting balance, 8% APR, $100 monthly payment, and 12 months—the monthly rate is 8 ÷ 1,200 = 0.0066667, or about 0.6667%.

1. Calculate the monthly growth factor: 1 + r = 1.0066667.
2. Raise it to 12 months: (1.0066667)¹² ≈ 1.082999.
3. Calculate the balance before subtracting payments: $20,000 × 1.082999 ≈ $21,659.98.
4. Calculate the accumulated value of the payments: $100 × [(1.082999 − 1) ÷ 0.0066667] ≈ $1,244.98.
5. Subtract: $21,659.98 − $1,244.98 = $20,415.00.

The estimated balance increase is $20,415.00 − $20,000 = $415.00. The figures are rounded to cents for display; calculations retain more precision before rounding.

Assumptions

• The interest rate stays fixed throughout the selected period.
• One payment is made at the end of each month.
• Interest compounds monthly at APR ÷ 12.
• The estimate excludes fees, taxes, insurance, PMI, escrow, and any changes in payment or rate.

How Negative Amortization Works

With ordinary amortization, a payment covers the interest accrued since the previous payment and then reduces principal. With negative amortization, the payment is less than that period’s interest. The shortfall is added to the balance, and subsequent interest can accrue on that larger amount. This is why a borrower may make payments yet owe more than the original principal.

For example, at an 8% annual rate on a $20,000 balance, the first month’s interest under this calculator’s assumptions is about $133.33. A $100 payment leaves about $33.33 unpaid, so the balance rises to roughly $20,033.33. Future interest is then calculated on the increased balance. The exact schedule can differ if a contract uses different timing, compounding, or payment rules.

When to Use This Estimate

Use the calculator to illustrate how a chosen payment and rate affect a balance over a defined period, or to compare hypothetical input combinations. It does not determine whether a specific contract permits unpaid interest to be added, how often a payment may change, or what happens when a balance reaches a contractual limit. Those details must come from the loan documents or lender’s disclosure.

Enter the principal balance at the beginning of the period being modeled—not necessarily the original amount borrowed. Enter APR as a percent per year, such as 8 for 8%, rather than as 0.08. The payment is the amount actually applied monthly in the scenario, and months is the number of monthly periods to project.

Limits, Costs, and Common Misunderstandings

A rising balance is the defining outcome of negative amortization, but a loan can have changing payments or other terms that this simple calculation cannot represent. It assumes every month has the same rate and payment and that unpaid interest is capitalized into the balance. It does not calculate a payment schedule with rate resets, payment caps, fees, additional principal payments, or a maximum balance. If the contract’s balance limit or payment rules matter, use the contract-specific figures rather than treating this estimate as a payoff quote.

• “A low payment always reduces principal.” Not necessarily. First, interest due must be covered; otherwise, the balance can grow.
• “The monthly payment is the monthly interest.” It is not. The interest amount depends on the outstanding balance and periodic rate, and the payment can be above or below it.
• “The result includes the full cost of borrowing.” No. The outputs show a modeled balance and its change, not every fee or other loan cost.
• “A balance increase means the calculator knows the contract terms.” No. It only shows the result of the inputs and stated assumptions.

For an actual account, check how the lender calculates interest, applies payments, and reports unpaid interest. Ask for the current principal balance and a written payment or balance projection if contract-specific details are needed. Do not treat the calculator as an approval, affordability, or loan-selection tool.

Frequently Asked Questions

What does negative amortization mean?
It means the scheduled payment does not cover all interest due, and the unpaid amount is added to the loan balance. The borrower can owe more than before even after making a payment.

How can I tell whether a loan has negative amortization?
Compare the payment with the interest charged for the period and check the loan documents for terms describing unpaid or deferred interest and its treatment. The lender can provide a statement showing how payments are applied.

Can negative amortization happen if I make every payment?
Yes. If a required or selected payment is below the interest accruing for that period, the difference may be added to the balance, subject to the loan’s terms.

Does negative amortization mean the loan is delinquent?
Not automatically. Negative amortization describes how the balance changes; whether a payment is considered late or the account is delinquent depends on the payment terms and account status.

What happens when payments later cover the interest?
Once a payment exceeds the interest due, the excess can begin reducing principal. The balance may still remain above its original amount until enough principal is repaid; the precise outcome depends on the loan terms.

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

Related

• Loan Amortization Excel With Extra Payments
• Loan Amortization: Definition, Formula and Example
• Loan Amortization Equation and Monthly Payment

in p | Starting loan balance | $ | 20000 | 1 | 100000000
in apr | Interest rate (APR) | % | 8 | 0.01 | 100
in pay | Monthly payment | $ | 100 | 0 | 100000000
in mos | Number of months | months | 12 | 1 | 600
out bal | Balance after period | $ | max(0, p * (1 + apr / 1200) ^ mos - pay * ((1 + apr / 1200) ^ mos - 1) / (apr / 1200)) | 2
out add | Balance increase | $ | bal - p | 2