How the loan payment is calculated
For a fixed-rate loan, the monthly payment is P × r ÷ (1 − (1 + r)−n). P is the amount borrowed, r is the monthly interest rate (the annual rate divided by 12) and n is the total number of monthly payments. If the rate is 0% the payment is simply the loan amount divided by the number of months.
The formulas, and what every variable means
payment = P × r ÷ (1 − (1 + r)−n)
interest for a month = current balance × r
principal for a month = payment − interest for that month
| Symbol | Meaning | How it is found |
|---|---|---|
| P | Principal: the amount you borrow | The loan amount you enter |
| r | Monthly interest rate | Annual rate ÷ 12 ÷ 100 (8% becomes 0.006667) |
| n | Number of monthly payments | Years × 12 (5 years is 60) |
| Balance | What you still owe | Starts at P and falls by the principal part of each payment |
Worked example 1, by hand: $25,000 at 8% for 5 years
- Monthly rate: r = 8 ÷ 100 ÷ 12 = 0.006667.
- Payments: n = 5 × 12 = 60.
- Growth factor: (1 + r)60 ≈ 1.4898.
- Payment: $25,000 × 0.006667 ÷ (1 − 1 ÷ 1.4898) ≈ $506.91 a month.
- Total paid: $506.91 × 60 = $30,415, so interest is $5,415.
Reading the schedule: the first three months
Each row splits the payment into interest and principal. Interest for a month is the current balance times the monthly rate. Whatever is left of the payment reduces the balance, so the next month's interest is slightly smaller. This is why extra payments are so effective: they shrink the balance that interest is charged on.
| Month | Payment | Interest | Principal | Balance |
|---|---|---|---|---|
| 1 | $506.91 | $166.67 | $340.24 | $24,659.76 |
| 2 | $506.91 | $164.40 | $342.51 | $24,317.25 |
| 3 | $506.91 | $162.11 | $344.79 | $23,972.45 |
In month 1, interest is $25,000 × 0.006667 = $166.67, so only $340.24 of the $506.91 payment reduces the loan.
Worked example 2: a personal loan, 3 years or 5?
A $10,000 personal loan at 12%.
| 3 years | 5 years | |
|---|---|---|
| Monthly payment | $332.14 | $222.44 |
| Total interest | $1,957 | $3,347 |
| Total paid | $11,957 | $13,347 |
The 5-year loan is $110 a month cheaper but costs $1,390 more in interest. If the higher payment fits your budget, the shorter loan is the better deal.
Worked example 3: adding $100 a month
Return to the $25,000 loan at 8% and add $100 to every payment, applied to principal.
| Regular payments | With $100 extra | |
|---|---|---|
| Time to pay off | 5 years | 4 years, 1 month |
| Total interest | $5,415 | $4,325 |
The extra $100 a month saves $1,089 and finishes the loan 11 months early.
Worked example 4: a one-time extra payment
Suppose you put a $2,000 tax refund toward the same loan in the first month. That saves $913 in interest and finishes the loan 5 months sooner. A lump sum early in the loan is worth more than the same amount paid near the end, because it stops interest from accumulating for longer. Use the "One-time extra payment" box above to test your own amount.
Common mistakes to avoid
- Judging a loan by the monthly payment alone. Compare total interest, as in example 2.
- Forgetting fees. Origination and closing fees raise the real cost of borrowing.
- Assuming extra payments go to principal. Ask your lender how to apply them.
- Using a variable-rate loan with a fixed-rate tool. The payment may change over time.
- Borrowing the maximum you are offered. Borrow what your budget supports.
Tips for borrowing less expensively
- Compare offers using APR, which includes most lender fees, not only the headline rate.
- Pick the shortest term whose payment fits comfortably in your budget.
- Pay a little extra each month if you can, and confirm it is applied to principal.
- Check your credit report before applying, since even a small rate difference adds up.
Buying a car? Try the auto loan calculator. Buying a home? Use the mortgage calculator. Carrying card debt? See the credit card payoff calculator.
Sources and review
The payment formula is the standard fixed-rate amortization formula, unit-tested against closed-form results. The Consumer Financial Protection Bureau explains how an amortizing loan and its schedule work: more of each early payment goes to interest, and the split shifts toward principal over time. Last reviewed September 2026. Read about our methodology.