Short answer: for a fixed rate loan with equal monthly payments, the payment is M = P x r / (1 - (1 + r)-n), where P is the amount borrowed, r is the yearly interest rate divided by 12 and n is the number of months. On $5,000 at 10% for 36 months that is $161.34 a month and $5,808.09 in total, the same example shown at the bottom of every page on this site.
The formula step by step
| Step | Example: $5,000, 10%, 36 months |
|---|---|
| 1. Monthly rate r = yearly rate / 12 | 0.10 / 12 = 0.0083333 |
| 2. Number of payments n | 36 |
| 3. (1 + r) to the power of minus n | 1.0083333-36 = 0.741740 |
| 4. 1 minus step 3 | 0.258260 |
| 5. P x r | 5,000 x 0.0083333 = 41.6667 |
| 6. Step 5 divided by step 4 | 41.6667 / 0.258260 = $161.34 |
Use the interest rate in this formula, not the APR. If the loan has an origination fee, the APR will be higher than the rate; see APR vs interest rate.
Where each payment goes: the payment schedule
In an amortizing loan, part of each monthly payment pays interest and part pays down the principal. Early payments are mostly interest; later payments are mostly principal (CFPB). Each month, interest = balance x r, and the rest of the payment reduces the balance.
| Period | Payment | Interest | Principal | Balance after |
|---|---|---|---|---|
| Month 1 | $161.34 | $41.67 | $119.67 | $4,880.33 |
| Month 2 | $161.34 | $40.67 | $120.67 | $4,759.66 |
| Month 3 | $161.34 | $39.66 | $121.67 | $4,637.99 |
| Year 1 total | $1,936.03 | $432.32 | $1,503.71 | $3,496.29 |
| Year 2 total | $1,936.03 | $274.86 | $1,661.17 | $1,835.12 |
| Year 3 total | $1,936.03 | $100.91 | $1,835.12 | $0.00 |
The rows for months 1 to 3 show single payments; the yearly rows add up 12 payments. Interest falls each year because the balance is lower.
Longer term, lower payment, more interest
| Term | Monthly payment | Total interest |
|---|---|---|
| 24 months | $230.72 | $537.39 |
| 36 months | $161.34 | $808.09 |
| 48 months | $126.81 | $1,087.02 |
| 60 months | $106.24 | $1,374.11 |
All rows: $5,000 at 10%. Stretching the loan from 36 to 60 months lowers the payment but adds $566.02 of interest (CFPB).
Payment and schedule calculator
| Month | Payment | Interest | Principal | Balance |
|---|
Checks before you rely on a number
- Real payments can differ by a few cents because lenders round each month and may adjust the last payment.
- Some loans charge interest daily, so paying late or early changes the interest slightly.
- The formula only fits fixed rate loans with equal payments. It does not fit a payday loan, which is due in one payment.
- The lender must show the payment schedule, the finance charge and the total of payments before you sign.
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Disclosure: Modern Lending Solutions is not a lender, loan broker or agent for any lender or loan broker, and does not make credit decisions. Any compensation we receive is paid by participating lenders, only for advertising services. This guide is general information, not financial or legal advice.