# What will my loan payment be?

Computes the level payment, total interest, and yearly schedule of a fixed-rate loan for any payment frequency and compounding.

- Page: https://www.acalculator.org/finance/loan-calculator
- JSON spec: https://www.acalculator.org/finance/loan-calculator.json
- Version: 9e634a147ad7

## Default answer

Example with the default inputs (Loan amount $25,000.00, Interest rate 7%, Loan term (years) 5, Payments Monthly, Interest compounds Monthly): A $25,000.00 loan at 7% over 5 years is repaid with 60 payments of $495.03, costing $4,701.80 in interest.

## Inputs

| Key | Label | Description |
| --- | --- | --- |
| amount | Loan amount | The amount borrowed. |
| rate | Interest rate | The nominal yearly interest rate, compounded as chosen below. |
| years | Loan term (years) | The length of the loan in years; decimals are allowed (2.5 is two and a half years). |
| freq | Payments | How often you pay: 12, 24, 26, 52, 4, or 1 times a year. |
| comp | Interest compounds | How many times a year interest is compounded: 365, 12, 4, 2, or 1. |

## Outputs

| Key | Label | Description |
| --- | --- | --- |
| payment | Your payment | The level payment made at each payment date (monthly, weekly, and so on, as chosen). |
| payments | Number of payments | How many payments repay the loan. |
| amount | Loan amount | The amount borrowed. |
| interest | Total interest | All the interest paid over the life of the loan. |
| paid | Total of payments | The loan amount plus all the interest. |
| perPayment | Rate per payment | The interest rate charged for each payment period, from the yearly rate and the compounding. |
| effective | Effective yearly rate | The yearly rate with compounding counted: (1 + rate per payment) to the power of payments a year, minus 1. |

## Method

payment = L × i ÷ (1 − (1 + i)^−n), with L the loan, n = round(years × payments a year), and i = (1 + r/m)^(m/p) − 1 the rate per payment for a yearly rate r compounded m times a year and p payments a year.

## Assumptions

- The rate is fixed for the whole loan.
- Payments are equal and made at the end of each payment period.
- Interest for each payment period is the balance times the rate per payment.
- The number of payments is the term in years times the payments a year, rounded to a whole number.
- The last payment is whatever is left; values are not rounded to the cent between payments.

## Worked examples

1. amount = $20,000.00, rate = 7%, years = 5, freq = 12, comp = 12 gives payment = $396.02, interest = $3,761.44, payments = 60, effective = 7.229008%. Source: hand calculation in content.mdx; Python 3 cross-check in docs/progress/WP-31/python/loan.py.
2. amount = $20,000.00, rate = 7%, years = 5, freq = 26, comp = 12 gives payment = $182.49, payments = 130, interest = $3,724.23. Source: hand calculation in content.mdx: rate per payment (1 + 0.07/12)^(12/26) − 1.
3. amount = $10,000.00, rate = 6%, years = 3, freq = 4, comp = 4 gives payment = $916.80, payments = 12, perPayment = 1.5%, interest = $1,001.60. Source: hand calculation in content.mdx: 10,000 × 0.015 ÷ (1 − 1.015^−12).
4. amount = $12,000.00, rate = 0%, years = 2.5, freq = 52, comp = 365 gives payment = $92.31, payments = 130, interest = $0.00. Source: hand calculation in content.mdx: 12,000 ÷ 130.

## FAQ

### How is a loan payment calculated?

A fixed-rate loan is repaid in equal payments. Each payment is L × i ÷ (1 − (1 + i)^−n), where L is the amount borrowed, i is the interest rate for one payment period, and n is the number of payments. For $20,000 at 7% over 5 years, paid monthly, i = 0.07 ÷ 12 and n = 60, so the payment is $396.02.

### What does the compounding choice change?

It sets how the yearly rate turns into a rate per payment. If interest compounds as often as you pay (monthly with monthly payments), the rate per payment is the yearly rate divided by the payments a year. If it compounds on a different schedule, the page uses the equivalent rate (1 + r/m)^(m/p) − 1. Most US consumer loans quote a rate that compounds monthly, which is the default.

### Do payments every two weeks save money?

Paying every two weeks over the same term means 26 smaller payments a year instead of 12. The money reaches the lender a little sooner, so the interest is a little lower: $20,000 at 7% over 5 years costs $3,761.44 of interest paid monthly and $3,724.23 paid every two weeks. The bigger saving in "biweekly" plans comes from the 13th monthly payment they add each year, which the amortization calculator can show as an extra yearly payment.

### What is the effective yearly rate?

It is the rate you really pay in a year once compounding is counted: (1 + rate per payment)^(payments a year) − 1. A 7% rate compounded monthly is an effective 7.229% a year. It lets you compare loans that compound differently.

### What is the difference between the interest rate and the APR?

The interest rate is the cost of borrowing the money. The APR (annual percentage rate) also counts fees such as origination fees, so it is usually higher. This page works from the interest rate. To see how a fee changes the APR, use the personal loan or business loan calculator.

### Can the loan term be a fraction of a year?

Yes. Type 2.5 for two and a half years. The page multiplies the years by the payments a year and rounds to a whole number of payments, so 2.5 years of weekly payments is 130 payments.

## Sources

- Consumer Financial Protection Bureau, What is the difference between a loan interest rate and the APR? https://www.consumerfinance.gov/ask-cfpb/what-is-the-difference-between-a-loan-interest-rate-and-the-apr-en-733/
- Consumer Financial Protection Bureau, What is amortization and how could it affect my auto loan? https://www.consumerfinance.gov/ask-cfpb/what-is-amortization-and-how-could-it-affect-my-auto-loan-en-771/
- Equivalent rates and the amortized loan payment: S. A. Broverman, Mathematics of Investment and Credit, chapter 1 (nominal and effective rates) and chapter 3 (amortization).