How the monthly payment is worked out
Personal loans, auto loans, and most student loans with a fixed rate use one formula. The lender sets a single payment for the whole term. Each month, interest on the remaining balance comes out first. The rest of the payment reduces what you owe.
M = P × r × (1 + r)n ÷ ((1 + r)n − 1)P = amount borrowed
r = APR ÷ 12 ÷ 100 (monthly rate)n = number of monthly paymentsRun the sample loan above through by hand: $18,500 at 9.4% over 60 months.
- Monthly rate
0.094 ÷ 12 = 0.007833 - Growth factor
(1.007833)60 = 1.59707 - Top line
18,500 × 0.007833 × 1.59707 = 231.44 - Payment
231.44 ÷ 0.59707 = $387.63
Why the first year feels slow
Interest is charged on the balance, and the balance is highest at the start. On the sample loan, $144.92 of the first $387.63 payment goes to the lender as interest. By month 48 the interest share has dropped to $37.39.
Half of all interest on this loan is paid by month 19, less than a third of the way through. The first year alone costs $1,610.18 in interest. Extra payments made early do the most work for this reason.
| Month | Interest | Principal | Balance after |
|---|---|---|---|
| 1 | $144.92 | $242.71 | $18,257.29 |
| 12 | $123.16 | $264.47 | $15,458.61 |
| 30 | $83.28 | $304.35 | $10,327.72 |
| 48 | $37.39 | $350.24 | $4,423.14 |
| 60 | $3.01 | $384.62 | $0.00 |
Longer terms lower the payment and raise the bill
Dealers and lenders often sell a loan by its monthly figure. Here is the same $18,500 at 9.4% across five terms.
| Term | Monthly payment | Total interest | Interest vs 36 months |
|---|---|---|---|
| 36 months | $591.75 | $2,802.83 | baseline |
| 48 months | $463.90 | $3,766.96 | +$964.13 |
| 60 months | $387.63 | $4,757.86 | +$1,955.03 |
| 72 months | $337.16 | $5,775.30 | +$2,972.47 |
| 84 months | $301.42 | $6,819.04 | +$4,016.21 |
Going from 60 to 84 months trims the payment by $86.21 and adds $2,061.18 in interest. The table holds the rate at 9.4% for every term. Real lenders charge more for longer terms, so the true gap is wider. On a car, a 7-year loan also raises the odds of owing more than the car is worth for several years.
The fee the rate leaves out
Many personal loan lenders charge an origination fee, often somewhere between 1% and 10% of the loan. Most take the fee out of the payout. You repay the full amount on paper but receive less cash.
Put a 5% fee on the sample loan. You receive $17,575, repay $18,500 plus interest, and the 9.4% rate becomes an effective 11.63% APR. On a 36-month term the same fee pushes the effective rate to 12.95%, because the fee is spread over fewer months.
In the US, the Truth in Lending Act requires lenders to show an APR with most fees included. Compare APR against APR, never one lender's rate against another's APR. Enter the fee above and the ticket shows the real figure.
Extra payments: check two clauses first
Adding $100 a month to the sample loan clears the balance in 46 months instead of 60 and saves $1,218.22. Adding $50 saves $700.70 and 8 months. Before you send more than the minimum, read the agreement for these:
- Prepayment penalty. A charge for paying early. Most mainstream personal loans have none, but some auto and subprime loans do.
- Precomputed interest. Some loans fix the total interest at signing, sometimes under the Rule of 78s. Paying early saves far less than this calculator shows.
- How extra money is applied. Some servicers treat extra cash as next month's payment paid in advance. Ask for the extra to go to principal, then check the next statement.
Where this calculator stops
- Fixed rates only. A variable-rate loan resets. Run each rate period as a separate loan using the balance left at the reset.
- Monthly interest, not daily. Many auto lenders charge simple interest by the day. Paying a few days early or late moves the numbers by a few dollars.
- No balloon payments, deferral, or payment holidays. Loans with a large final payment need a different model.
- No add-ons. GAP cover, credit insurance, and service contracts rolled into a car loan raise the balance. Add them to the amount borrowed.
- Home loans need more. Property tax, insurance, and PMI belong in the mortgage calculator.
- Credit cards do not fit. A card balance has no fixed term, so a set payment schedule does not describe the debt.
Your lender's loan disclosure is the binding figure. Expect this page to land within a few dollars of the disclosure when the terms above line up.
Five numbers to find on any loan offer
- APRThe rate with fees folded in. Use this to compare lenders.
- Amount financedThe cash you receive after fees. Compare against the loan amount.
- Term in monthsLonger terms cost more in total, even at the same rate.
- Total of paymentsEverything you will pay over the life of the loan.
- Prepayment termsWhether paying early saves interest or costs a penalty.
