What Is a Reverse Amortization Calculator?

A reverse amortization calculator works the loan equation backwards. An ordinary amortisation schedule starts with three knowns, the principal, the rate and the term, and produces the payment. A reverse amortisation solves the opposite problem: you already know what you can pay, or what the lender is asking, and you need to know how long the loan will last, how much it supports, or what rate is really being charged.

The three questions are the ones borrowers and analysts ask most often. How many payments before this is clear? What size loan does this payment support at this rate? And what interest rate is implied by a quoted payment and term? All three rest on the same amortising payment relationship, rearranged for a different unknown, and all three are exactly solvable except the rate.

How It Works

The core relationship is the standard amortising payment: the principal multiplied by the periodic rate, divided by one minus one plus the periodic rate raised to the power of the negative number of payments. Solving it for the term rearranges to the negative natural logarithm of one minus the monthly rate times the principal divided by the payment, all divided by the natural logarithm of one plus the monthly rate.

Solving for the principal simply multiplies the payment by one minus one plus the monthly rate to the power of the negative term, divided by the monthly rate. Solving for the rate has no algebraic inverse, so the calculator uses bisection: it checks that the target payment lies between what a very low rate and a very high rate would require, then repeatedly halves the interval. Two hundred halvings converge to a precision far beyond anything a contract needs.

Every solution is then projected month by month rather than left as a formula. Each month the outstanding balance is charged interest at the monthly rate, the payment is applied to that interest first and to principal second, and any extra payment or annual step-up is added before the balance is recalculated. A final part-payment is capped at the remaining balance, which is why the last instalment shown differs from the scheduled amount.

Two guards matter in practice. If the payment is smaller than the first month's interest, the balance grows rather than shrinks and no term exists, so the calculator reports that the loan never clears instead of returning a huge number. And when the implied rate falls outside a plausible range, the tool says so rather than presenting an answer it cannot support.

Understanding Your Results

The primary card shows the value being solved for: the payoff term, the principal the payment supports, or the implied annual rate, with the scheduled payment and the date the loan finishes underneath. The three statistics beside it give the total interest, the number of payments, and the effective annual rate, which is the nominal monthly rate compounded twelve times and is always slightly above the nominal figure you entered.

The breakdown table projects the loan year by year, showing what was paid, how it split between interest and principal, and the balance still outstanding, with a total row at the bottom. Summary Statistics collects the principal, nominal, monthly and effective rates, the scheduled and extra payments, the term and payoff date, the total paid, the total interest and its share of the principal, the final instalment, and the comparison against making no extra payments at all: the months and the interest that the extra money saves.