Loan How to Calculate a Personal Loan Payment by Hand
One formula, five minutes: M = P x r(1+r)^n / ((1+r)^n - 1) worked digit by digit on a $10,000 loan at 10% — $322.67 a month — plus the fee adjustment lenders hope you skip and the zero-rate shortcut.
How-to · Published November 7, 2026 · Loan Calculations
Every personal loan quote you will ever receive comes out of one formula. Lenders run it on their side of the desk; this page puts it on yours. Learn it once — with a phone calculator, in about five minutes — and no payment quote ever has to be taken on trust again, because you can reproduce the number, and a number you can reproduce is a number you can check.
The formula, with every letter defined
M = P × r(1+r)n / ((1+r)n − 1)
- P — the amount financed: what the loan is calculated on.
- r — the monthly rate: APR / 100 / 12.
- n — the number of monthly payments.
- M — the monthly payment the formula returns.
That is the entire machine. Everything below is arithmetic and consequences.
The worked example, step by step
Our example — the same one our Personal Loan Calculator uses — is $10,000 at 10% APR for 36 months.
- Convert the rate. r = 10 / 100 / 12 = 0.008333. The formula needs the monthly rate because payments — and interest charges — happen monthly.
- Raise (1 + r) to the n. This is the step where people get lost, so do it literally: (1.008333)36 means 1.008333 multiplied by itself 36 times. On a phone calculator, use the power key (xy): 1.008333, power, 36. The result is about 1.3490. What this number represents is growth: what $1 becomes after 36 months of monthly compounding at this rate.
- Build the numerator. P × r × (1+r)n = 10,000 × 0.008333 × 1.3490 = 112.41 (approximately).
- Build the denominator. (1+r)n − 1 = 1.3490 − 1 = 0.3490.
- Divide. M = 112.41 / 0.3490 = $322.67 a month.
Turning the payment into the truth
The payment is the quote; the cost is what the payment hides. Two multiplications expose it: total of payments = M × n = $11,616.19, and total interest = total − P = $1,616.19. (If your M × n lands a few cents off these totals, that is rounding — the calculator carries the unrounded payment through; your $322.67 is the rounded display of the same number.) A lender who quotes only the $322.67 is showing you the smallest true number available. The $1,616.19 is the price of the loan, and you computed it yourself.
The zero-rate shortcut
If r = 0, the formula divides by zero — the numerator and denominator both collapse. That is not a failure; it is the formula telling you there is no interest to model. At a true zero rate the payment is simply P / n: the amount split evenly across the payments, nothing more. Any "0% offer" whose payment is higher than P / n has something else inside it — usually a fee — which is the next section.
The fee adjustment, in numbers
Fees change the answer in one of two ways, depending on how they are charged. If the fee is financed — added to the loan — run the formula on the amount plus the fee. On our worked loan, a 5% fee on $10,000 makes the balance $10,500, and the same formula returns a payment of $338.81 — even though you received $10,000. If the fee is paid upfront instead, the payment is unchanged at $322.67, but the honest rate is not 10% anymore: you paid for the loan before it started. That gap between the quoted rate and the honest rate is exactly what an APR measures, and it is what the APR Calculator prices.
The extra-payment line
The formula returns the contract payment — the minimum that retires the loan in exactly n months. Paying more rewrites the ending. On the worked loan, $50 a month extra ends it in 31 months instead of 36 and saves $249.88 of interest: five payments that never happen, because every extra dollar went to principal and shrank every later interest charge. The contract formula cannot show you this — it assumes the contract — which is why the calculator models extra payments alongside it.
Checking a lender's quote
Here is the whole page in one habit. A quote gives you P, the rate and the term. Run the formula. If the lender's M matches yours, the quote is the loan you think it is. If their M differs from yours by more than rounding, then one of the three inputs is not what you were told — the amount financed includes something extra, the rate is not the rate, or the term is not the term. Find out which before signing, because after signing, the formula works for the contract, not for you. The Loan Calculator runs the same formula backwards — payment in, amount, term or rate out — for checking quotes from the other direction.
Frequently asked questions
Why does the formula use a monthly rate?
Because payments are monthly, so interest is charged monthly. The conversion is annual rate / 12 — r = APR / 100 / 12 — and it has to happen before anything else in the formula, or every later step inherits the error.
What if my loan quotes a flat or add-on rate instead of APR?
Some lenders quote add-on interest, which is a different and more expensive structure: interest charged on the original amount for the whole term, regardless of what you have repaid. The check is this formula — a payment that matches it at the quoted rate is an amortizing loan at that rate; a payment that doesn't match is something else wearing the rate as a label.
Can I use this for a car loan or a mortgage?
Yes. It is the same amortization formula for every fixed-rate installment loan — car, mortgage, personal. Only the extras around it change: fees, taxes, insurance, and in a mortgage's case an escrow line. The core arithmetic is identical.