Reverse Amortization Calculator by Payment

This reverse amortization calculator estimates how many monthly payments it takes to repay a loan when you enter the balance, APR, and monthly payment. It also shows the estimated payoff time in years and the total paid using that payment amount.

Formula

The calculator reverses the standard fixed-payment amortization equation to solve for the number of monthly payments. It first calculates the monthly interest rate, then determines the number of payment periods required to reduce the balance to zero:

n = ceil(round(-ln(1 - r × P / M) / ln(1 + r), 6))

• P is the starting loan balance in dollars.
• APR is the annual percentage rate entered as a percent per year.
• r is the monthly rate, calculated as APR / 1200.
• M is the monthly payment in dollars.
• n is the number of monthly payments, rounded up to a whole payment.

The calculator then estimates total paid as n × M and estimated interest as n × M − P. Because it rounds the number of payments up, the last payment may in reality be smaller than the regular payment. The total and interest outputs are therefore estimates based on making the entered amount for every counted month.

Worked Example

Using the calculator’s defaults: a $20,000 balance, 8% APR, and a $500 monthly payment.

1. Convert APR to a monthly rate: r = 8 / 1200 = 0.0066667.
2. Substitute into the reverse amortization formula: n = ceil(round(-ln(1 − 0.0066667 × 20,000 / 500) / ln(1.0066667), 6)).
3. Evaluate the expression: the unrounded period is about 47.1 months, so the calculator rounds up to 48 payments.
4. Convert to years: 48 / 12 = 4.00 years.
5. Estimate total paid: 48 × $500 = $24,000.
6. Estimate interest: $24,000 − $20,000 = $4,000.

So, with these inputs, the calculator returns 48 monthly payments, about 4.00 years, $24,000 paid, and $4,000 in estimated interest.

Assumptions

• The interest rate stays fixed for the full calculation.
• Payments are made monthly, with the first payment one month after the starting balance is measured.
• Interest compounds monthly at APR divided by 12.
• The model excludes fees, taxes, insurance, PMI, escrow, late charges, and changes to the payment or balance.

When to Use a Reverse Amortization Calculator

Use this calculation when you know the current amount owed and a proposed monthly payment, but want to estimate the payoff duration. It answers a different question from a regular amortization calculator: a regular calculator commonly takes the loan term as an input and solves for the payment, while this one takes the payment as an input and solves for the number of months.

It can help with simple planning comparisons, such as checking how a higher or lower payment changes the estimated time to repay. Keep the other inputs unchanged when comparing results so the payment is the only changing variable. For a real account, use the current payoff balance and the rate and payment treatment stated in the lender’s records; a displayed balance may not be the exact amount required to settle the loan on a particular date.

How to Read the Result

“Payments to repay” is rounded up to a whole month because a loan generally cannot be fully repaid in a fraction of a scheduled monthly payment. The years figure is simply that month count divided by 12. For example, 30 months is 2.50 years.

The displayed total paid assumes the entered payment is made in every counted month. In actual amortization, the final payment often only covers the remaining principal and interest, so it may be less than the regular payment. The estimated interest output inherits that simplification. A detailed payoff schedule would calculate each month’s interest and adjust the final payment rather than count every payment at the full entered amount.

Common Problems and Limits

• Payment does not cover interest: At the stated rate, the monthly interest on the starting balance is P × r. If the payment is no greater than that amount, the balance will not decline under this fixed-payment model, so there is no finite payoff time.
• APR entered in the wrong units: Enter 8 for 8%, not 0.08. The formula divides the entered percentage by 1,200 to obtain a monthly decimal rate.
• Using the wrong balance: An original loan amount may differ from the balance remaining today. Use the balance corresponding to the date from which the estimate should begin.
• Changing terms or charges: Variable rates, skipped or irregular payments, fees added to the balance, and payment changes are not represented.
• Rounding differences: Lenders may calculate daily interest, use specific due dates, or handle cents and final payments differently. This simplified monthly model can therefore differ from an account statement.

The formula assumes a positive APR because it uses the monthly-rate form of the amortization equation. It is not a substitute for a lender’s payoff quote or transaction-level payment schedule.

Frequently Asked Questions

What does a reverse amortization calculator calculate?
It estimates the number of monthly payments needed to repay a balance at a stated APR and monthly payment. It can also estimate payoff time and total paid.

What if my payment is less than the monthly interest?
The balance will not be paid down under the calculator’s fixed-rate assumptions. If the payment only equals monthly interest, the balance stays level; if it is lower, the balance grows.

Does the calculator include a smaller final payment?
No. Its total-paid estimate counts the entered payment for every whole month. The actual last payment may be smaller, so the model can slightly overstate total paid and interest.

Can I use this for a variable-rate loan?
Only as a simplified estimate using one APR for the whole period. The result will not reflect future rate changes, payment recalculations, or other contract terms.

Why does my lender’s payoff date differ?
The lender may use daily interest, different payment dates, fees, a changing rate, or a smaller final payment. The calculator also rounds the term to a whole number of months.

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

Related

• Daily Payment Amortization Schedule Calculator
• Deferred Payment Amortization Schedule Calculator
• Car Payment Amortization With Extra Payments

in p | Loan balance | $ | 20000 | 0.01 | 100000000
in apr | Interest rate (APR) | % | 8 | 0.01 | 100
in pay | Monthly payment | $ | 500 | 0.01 | 100000000
out mos | Payments to repay | months | ceil(round(-ln(1 - (apr / 1200) * p / pay) / ln(1 + apr / 1200), 6)) | 0
out yrs | Estimated payoff time | years | mos / 12 | 2
out tot | Total paid | $ | mos * pay | 2
out int | Estimated total interest | $ | mos * pay - p | 2