Loan APR vs Flat Rate Converter
Enter any flat-rate loan offer. Get the true reducing-balance APR so you can compare honestly.
How a Flat Rate Is Actually Calculated
A flat interest rate applies a fixed percentage to the original principal for every year of the loan, regardless of how much you have already repaid. If you borrow $10,000 at 10% flat for three years, the lender multiplies $10,000 × 10% × 3 = $3,000 in interest, then divides the combined $13,000 into 36 equal monthly instalments of roughly $361. Simple arithmetic. No compounding, no diminishing balance.
The problem is buried in what "10%" actually implies. In month one, you owe $10,000 — so paying $149 in interest (the equivalent reducing-balance charge at the true APR) is fair enough. But in month 35, after you have repaid almost everything, your outstanding balance is barely $355 — yet the flat-rate schedule still charges you as though the full $10,000 remains at risk. You are paying interest on money you returned two years ago. That asymmetry is why a 10% flat rate translates to a 17.9% nominal APR on a reducing balance.
The Maths Behind the Conversion
Converting a flat rate to an APR requires solving what actuaries call the internal rate of return (IRR) of the loan's cash flows. You know the loan amount (a lump sum today), and you know each monthly payment. The APR is the monthly discount rate that makes the present value of all future payments exactly equal to the sum you borrowed today.
Formally, if P is the principal, M is the fixed monthly payment, r is the monthly interest rate and n is the number of months:
P = M × [1 − (1 + r)^−n] / r
There is no algebraic closed form for r. You solve it numerically — the calculator above uses bisection, bracketing the monthly rate between near-zero and an absurdly high ceiling, then halving the interval 200 times until the precision is within 0.000000001%. Once you have the monthly rate, the nominal APR is simply that rate multiplied by 12, which is the figure regulators in most countries require lenders to disclose. The effective annual rate (EAR) compounds that monthly rate: (1 + r)¹² − 1, which is the truer measure of what compounding costs you over a full year.
The Multiplier Rule of Thumb — and Why It Fails
Bankers and brokers sometimes quote a rule of thumb: the true APR on a flat-rate loan is "approximately double the flat rate." For a 24-month loan this approximation is reasonably close. But for a 60-month car loan it understates the APR, and for a 12-month personal loan it can overshoot. The precise relationship is:
Approximate EAR ≈ 2 × n × flat_rate / (n + 1)
where n is the number of monthly payments. For 36 payments at 10% flat: 2 × 36 × 0.10 / 37 = 19.46% — which matches the effective rate almost exactly for this term length. But at 60 months and 5% flat the formula gives 9.84% while the exact bisection method yields 9.55%. For anything beyond back-of-envelope work — especially before signing a loan agreement — use the exact numerical approach.
Flat Rates Are Not Inherently Predatory
It would be unfair to characterise flat-rate quoting as purely deceptive. Flat rates are genuinely simpler to communicate: a salesperson explaining "you pay $361 a month for 36 months on a $10,000 loan" is unambiguous. The monthly cash flow is fixed, and a buyer with a strict budget can immediately check affordability. The issue arises when borrowers compare a flat-rate quote from lender A with an APR quote from lender B and assume the lower number is the cheaper loan. That comparison is like reading a car's fuel consumption in miles-per-gallon versus litres-per-100km and picking the lower number.
Many jurisdictions — the EU's Consumer Credit Directive, the UK's Consumer Credit Act, the US Truth in Lending Act (TILA), and India's RBI fair practices code among them — now mandate that lenders disclose the APR alongside any advertised rate. But advertisements still lead with the flat rate, dealers still frame conversations around monthly payments rather than total cost, and the cognitive gap persists.
Early Repayment and the Rule of 78
Flat-rate loans introduce a second, less obvious trap when you try to settle early. Because interest was front-loaded into equal monthly instalments, you might assume that paying off after 18 months of a 36-month loan saves you half the remaining interest. But some lenders apply the Rule of 78s (also called the sum-of-digits method) to calculate how much of the interest you have "consumed." The name comes from the sum of digits 1 through 12 equalling 78; for a 12-month loan, the lender assigns the first month 12/78 of the total interest, the second month 11/78, and so on — making you pay interest faster than a straight reducing-balance schedule would. On a 36-month loan the denominators sum to 666, and the front-loading is heavier still. The practical result: even if a flat-rate lender agrees to an early settlement, the rebate of remaining interest is smaller than you expect, and the effective cost of the loan rises if you leave early.
Reading the Amortization Table
The amortization schedule produced by this calculator (click "Show Amortization Table" after conversion) illuminates the internal mechanics that flat-rate marketing conceals. In the first few months on a true reducing-balance schedule, the majority of your payment services interest, with only a small slice reducing principal. Over time that ratio flips — which is why the outstanding balance falls slowly at first and then rapidly toward the end. This is a mathematical inevitability of compound interest, not a lender trick. But comparing the reducing-balance table against what a flat-rate borrower actually experiences reveals the distortion: on a flat-rate loan the interest charged per month is exactly totalInterest/months — a constant — rather than the steeply front-loaded then declining curve of a proper amortization. The cash flows are identical; the accounting label "interest" versus "principal" is what differs, and that label determines how much rebate you receive on early exit.
Practical Decision Rules
Before accepting any loan offer, convert every quote to the same basis — APR on a reducing balance — using this tool or the lender's mandated disclosure. A loan advertised at 7% flat over 4 years carries a nominal APR of around 13.1%; if a rival lender quotes 12.5% APR on a reducing balance, the flat-rate loan is actually more expensive despite its lower headline number. When comparing two APR figures, verify whether they are nominal (monthly rate × 12) or effective (compounded). For the same loan, the effective rate is always slightly higher than the nominal rate; the difference grows with term length. Finally, factor in any arrangement fees, which many jurisdictions require lenders to include in their APR calculation but which may be omitted from the flat-rate headline. A loan with a £200 processing fee on a £5,000 principal at 6% flat looks different once that fee is folded into the IRR calculation — the true APR jumps accordingly. Transparency about the total cost of credit, in a single comparable metric, is the only way to make an honest choice.
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