Payment Calculator: How It Works
This calculator solves the standard instalment equation in whichever direction you need: give it an amount and get the payment, or give it a payment and get the term. It is the general-purpose tool behind every loan, lease and instalment plan with a fixed periodic payment.
One equation, four variables
Any fixed-payment agreement links four quantities: present value (what you borrow), the periodic rate, the number of periods, and the payment. Fix any three and the fourth is determined:
PMT = PV × r ÷ [1 − (1 + r)−n]
Rearranged to solve for the number of periods:
n = −log(1 − PV × r ÷ PMT) ÷ log(1 + r)
The second form is the more useful one in practice. It answers the question people actually have — if I can pay this much a month, how long will this take? — and it is the calculation credit card statements are legally required to show for minimum payments.
Matching the rate to the period
The most common error is a mismatch between r and n. The rate must be per period, and the periods must be counted, not measured in years.
| Payment frequency | r from a 12% annual rate | n for 5 years |
|---|---|---|
| Monthly | 0.12 ÷ 12 = 0.01 | 60 |
| Fortnightly | 0.12 ÷ 26 = 0.004615 | 130 |
| Weekly | 0.12 ÷ 52 = 0.002308 | 260 |
| Quarterly | 0.12 ÷ 4 = 0.03 | 20 |
Why fortnightly payments quietly shorten a loan
Paying half the monthly amount every fortnight is not the same as paying monthly. There are 26 fortnights in a year but only 12 months, so you make the equivalent of 13 monthly payments instead of 12. On a 25-year loan that single extra payment per year typically removes four to five years and a large share of the interest — without any month ever feeling different. If your lender allows it at no extra cost, it is one of the cheapest wins available.
A worked example: solving for term
You owe 8,000 on a card at 19.9% APR and can pay 250 a month. Monthly r = 0.199 ÷ 12 = 0.016583.
n = −log(1 − 8000 × 0.016583 ÷ 250) ÷ log(1.016583) ≈ 39 months, with roughly 1,750 of interest.
Raise the payment to 350 and it becomes 26 months and about 1,120 of interest. Drop it to 175 and the term stretches past 70 months with more than 4,200 in interest. The relationship is sharply non-linear — small increases in payment produce large reductions in cost.
When there is no solution
If your payment is less than or equal to the interest accruing each period, the balance never falls and the equation has no answer. On the 8,000 example above, monthly interest is 8,000 × 0.016583 = 132.66, so any payment at or below that leaves the debt permanent or growing. If a calculator returns an error or an impossible term, this is almost always why.
Beyond loans
The same arithmetic covers equipment leases, buy-now-pay-later plans, instalment sales and structured settlements. Anywhere a fixed amount recurs against a balance carrying interest, this equation applies — which is why spreadsheets expose it as a single function, PMT(), and why understanding it once covers most consumer finance you will ever meet.