What makes up an installment?
In a conventional equal-payment loan, each installment contains a principal portion and a periodic finance-charge portion. With a fixed rate, their sum remains constant, but the interest portion generally falls as the balance declines while the principal portion rises. This process is called amortization.
The formula and its symbols
- M: monthly payment.
- P: principal financed after any down payment.
- r: periodic monthly rate as a decimal. For a 6% nominal annual rate, r = 0.06 ÷ 12 = 0.005.
- n: number of monthly payments. Three years gives n = 3 × 12 = 36.
The formula assumes equal end-of-month payments, a fixed rate, and no fees, balloon payment, or early settlement. A contract with different features needs its actual terms.
A complete numerical example
Calculate a 60,000 loan at a 6% nominal annual rate over three years:
- Monthly rate: 0.06 ÷ 12 = 0.005.
- Payment count: 36.
- Substitute: M = 60,000 × 0.005 × (1.005)36 ÷ [(1.005)36 − 1].
- The payment is approximately 1,825.32.
- Total installments are about 65,711.38, with estimated interest of about 5,711.38 before fees.
The final contractual installment can differ slightly because of rounding in the actual schedule.
How the payment splits in an amortization schedule
First-month interest is 60,000 × 0.005 = 300. The rest of the payment reduces principal. The next month uses the new balance rather than the original 60,000.
| Month | Opening balance | Interest | Principal repaid | Closing balance |
|---|---|---|---|---|
| 1 | 60,000.00 | 300.00 | 1,525.32 | 58,474.68 |
| 2 | 58,474.68 | 292.37 | 1,532.94 | 56,941.74 |
| 3 | 56,941.74 | 284.71 | 1,540.61 | 55,401.13 |
The payment stays constant, but interest falls and principal repayment rises. That is the correct way to read the schedule.
What a longer term changes
Increasing n usually reduces the payment because principal is spread over more installments, but it also gives interest more periods to accumulate. Compare total installments and total finance cost, not the payment alone. A complete comparison appears in the financing-cost guide.
Common mistakes
- Using 6 instead of 0.06, or forgetting to convert the annual rate to a monthly rate.
- Using years rather than the number of monthly payments.
- Calculating every month's interest on the original balance.
- Entering the asset price instead of principal after the down payment.
- Assuming the installment includes fees or insurance without checking.
Frequently asked questions
Can I just divide principal plus interest by the number of months?
That shortcut does not accurately model an amortizing loan because interest changes with the balance. Use the amortization formula for the model described here.
What if the rate is zero?
The formula's denominator becomes zero. The direct payment is simply P ÷ n.
Is the calculator schedule a contractual disclosure?
No. It is an educational model. The lender's official schedule contains the actual fees, timing, rounding, and terms.
Sources and references
- CFPB — Auto loan key terms: amortization and the split between principal and finance charge. Accessed 2026-11-06.
- Figures use the fixed-rate loan formula and are displayed to two decimals. Examples are not financing offers.