Reverse Amortization Table for a Loan: How It Works

A reverse amortization table shows a loan’s balance moving backward from a known future balance or payoff point to an earlier date, rather than listing scheduled payments from the start. This calculator estimates the balance at the start of a level-payment loan from its payment, annual interest rate, and term; it also shows the implied original principal and total interest.

Formula

For a fixed-rate loan with equal monthly payments, the present value of all future payments is the implied original loan amount. The reverse-amortization formula is:

PV = PMT × [1 − (1 + r)⁻ⁿ] ÷ r

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

The calculator’s second result estimates total interest as PMT × n − PV. The formula assumes each payment is made at the end of a month and that the stated payment is the full scheduled principal-and-interest payment. It reverses the standard level-payment loan formula; it does not infer a real loan’s terms from a payment if fees, insurance, or other charges are bundled into that payment.

Worked Example

Using the defaults—monthly payment $405.53, APR 8%, and term 5 years—first convert the annual rate and term:

• Monthly rate: r = 8 ÷ 1,200 = 0.0066667.
• Number of payments: n = 5 × 12 = 60.

Substitute these values into the reverse formula:

PV = 405.53 × [1 − (1 + 0.0066667)⁻⁶⁰] ÷ 0.0066667 ≈ $19,999.91.

The estimated total interest is 405.53 × 60 − 19,999.91 = $4,331.89. The small difference from a round $20,000 principal results from using a payment rounded to cents. This example is a mathematical illustration, not a quote for a loan.

What a Reverse Amortization Table Shows

A conventional amortization table starts with the principal and records each payment, separating interest from the amount that reduces the balance. A reverse table works from known payment terms toward an implied starting balance, or from a known ending balance toward earlier balances. The phrase is not used in only one way: some readers mean reversing a standard schedule, while others mean a loan whose balance grows because payments are deferred or insufficient to cover interest. Those are different calculations.

This calculator addresses the first meaning: it estimates the starting principal from a fixed monthly payment, APR, and term. It does not model a growing-balance loan. To reverse a schedule by payment number, a separate balance formula can calculate the amount remaining after k payments: balance = PV × (1 + r)^k − PMT × [(1 + r)^k − 1] ÷ r. Here, k is the number of completed monthly payments.

When to Use the Estimate

The calculation can help check what principal is consistent with a stated payment, rate, and term, or explain how a payment schedule relates to principal and interest. It may also help identify a mismatch when comparing a quoted payment with loan terms, provided the quote is for level monthly principal-and-interest payments. Obtain the actual APR, payment, term, and any charges from the lender’s loan disclosure; do not treat a reverse estimate as a loan offer or account balance.

Use consistent inputs. Enter the monthly payment—not an annual payment—and APR as a yearly percentage, such as 8 for 8%, not 0.08. Enter the term in years. For a term stated in months, divide by 12 before entering it. If payments vary, occur on irregular dates, or include a balloon amount, this level-payment formula may not match the contract.

How to Read the Results and Common Errors

The first result is an implied starting principal, not the current balance or a payoff quote. Total interest is the sum of the assumed payments minus the implied principal over the full term. A real payoff amount can differ because it depends on the actual remaining balance, payment dates, accrued interest, and any applicable charges.

• Mixing rate formats: the calculator converts APR in percent to a monthly rate by dividing by 1,200. Entering 0.08 for 8% makes the assumed rate far smaller than intended.
• Using the wrong payment: an all-in monthly bill may include items besides principal and interest. Entering that entire bill overstates the principal the formula implies.
• Ignoring rounding: real payments are commonly expressed to cents. Rounding a payment can make the reconstructed principal differ slightly from the original amount.
• Assuming every loan amortizes evenly: interest-only periods, variable rates, skipped payments, extra payments, and balloon payments require a different schedule.

Limits and Other Loan Structures

The formula assumes a constant rate and equal payments at regular monthly intervals. It treats APR as a nominal annual rate divided by 12, matching the calculator’s stated monthly-rate convention. It does not account for changing rates, daily accrual, payment-date adjustments, fees financed into principal, or lender-specific rounding. If you know the actual principal and want a period-by-period schedule, use a standard amortization calculation instead.

A growing-balance or deferred-payment arrangement cannot be reconstructed with this calculator merely by calling it “reverse amortization.” Such a case needs its own inputs, including how interest accrues, whether unpaid interest is added to principal, payment rules, and the dates involved. Check the contract’s schedule and ask the servicer how its balance is calculated when those features apply.

Assumptions

• Interest rate is fixed for the full term.
• Payments are equal and made at the end of each month.
• Interest compounds monthly at APR ÷ 12.
• Fees, taxes, insurance, PMI, and escrow are not included.

Frequently Asked Questions

What is a reverse amortization table for a loan?
A reverse table works backward from known loan details to estimate an earlier balance or implied principal. The term can also describe growing-balance arrangements, which require a different model.

How do I calculate the original loan amount from a payment?
For fixed monthly payments, multiply the payment by [1 − (1 + monthly rate)^{−number of payments}] divided by the monthly rate. The result is an estimated starting principal under those assumptions.

Does this calculator show my current loan balance?
No. It estimates starting principal from payment, APR, and full term. A current balance requires the original loan details and the number and timing of payments already made.

Why might the estimate differ from my loan amount?
The payment may include other charges, the rate or term may be different, the loan may have variable or irregular payments, or rounding may affect the result. Check the lender’s disclosed terms and schedule.

Can this calculate a loan where the balance grows?
No. This calculator assumes payments reduce a fixed-rate loan over time. A growing balance depends on the contract’s interest accrual and payment rules and needs a separate calculation.

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

Related

• Amortization Table Software: Calculate Loan Payments
• Amortization Table Setup: Formula and Example
• Amortization Table Sample: Monthly Loan Breakdown

in pmt | Monthly payment | $ | 405.53 | 0.01 | 1000000
in apr | Interest rate (APR) | % | 8 | 0.01 | 100
in yrs | Loan term | years | 5 | 0.0833 | 50
out pv | Implied loan amount | $ | pmt * (1 - (1 + apr / 1200) ^ -(yrs * 12)) / (apr / 1200) | 2
out int | Total interest | $ | pmt * yrs * 12 - pv | 2