Debt Payoff Calculator

This calculator solves the amortization relationship for time rather than for payment. Starting from the present value of an ordinary annuity, B equals M times (1 minus (1 + r) to the power minus n) divided by r, and rearranging to isolate the exponent gives n equals minus the natural log of (1 minus B times r divided by M), divided by the natural log of (1 + r). Here B is the current balance, M the fixed monthly payment and r the monthly rate, the annual rate divided by twelve. The result is rounded up to a whole number of payments, so the final one is smaller than the rest. Total interest is simply M times n minus B. The formula carries a hard boundary that is worth understanding. The term inside the logarithm, 1 minus B times r divided by M, must stay positive, which means the payment must exceed the first month's interest charge of B times r. If it does not, the log is undefined and the debt never amortizes; the balance is flat or growing. On a 5,000 dollar balance at 19.99 percent, monthly interest is about 83 dollars, so any payment at or below that level never retires the principal. The model assumes a fixed payment, a fixed rate and no new charges - assumptions that hold for an installment loan but break on a credit card where the issuer's required minimum declines with the balance, where variable rates track the prime rate, and where any new purchase resets the calculation.

The arithmetic behind payoff timelines is older than consumer lending. Simon Stevin published interest tables in Dutch in 1582 and Richard Witt issued the first English book of compound interest tables in 1613, but neither could invert the relationship to solve for the number of periods. That became practical after John Napier introduced logarithms in 1614 and Henry Briggs published base-ten tables in 1624, since the exponent could then be extracted with a division of two logs. Edmond Halley extended the same annuity framework to life contingencies in 1693, and by the eighteenth century the present value of an annuity was standard actuarial equipment. Applying it to household borrowing is much more recent. Installment credit for consumer goods expanded sharply in the 1920s, but disclosure was inconsistent, and dealers often quoted an add-on rate that understated the true cost because the borrower did not have use of the full principal for the full term. The Truth in Lending Act of 1968 and its Regulation Z required lenders to compute and disclose the annual percentage rate on a consistent actuarial basis, which made payoff calculations comparable across products for the first time. The competing payoff orderings people argue about today were popularized later: the avalanche method follows directly from the interest arithmetic, while the snowball method, promoted by the personal finance writer Dave Ramsey from the 1990s, prioritizes the smallest balance for motivational reasons.