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Loan Payment Calculator

Calculate periodic loan payment amounts based on principal, interest rate, term, and payment frequency.

What this tool does

Calculate periodic loan payment amounts based on principal, interest rate, term, and payment frequency. You fill in these fields: Loan amount, Annual interest rate, Loan term, and Payments per year. It shows payment per period, total paid, total interest, and number of payments.

Inputs

  • Loan amount: A number. Must be greater than 0. The amount borrowed, or the balance still owed.
  • Annual interest rate (%): A number. Accepts 0 to 1,000. The yearly rate as a percentage. Enter 6.5 for 6.5 percent, or 0 for an interest-free loan.
  • Loan term (years): A number. Greater than 0, up to 100. How long the loan runs, in years. Part years are allowed, for example 2.5.
  • Payments per year: A whole number. Accepts 1 to 365. Starts at 12. How many payments are made each year. 12 is monthly, 26 is every two weeks, 4 is quarterly and 1 is yearly.

How to use

  1. Enter the loan amount.
  2. Enter the annual interest rate as a percentage.
  3. Enter the loan term in years.
  4. Enter the payments per year.
  5. Read the result: payment per period, total paid, total interest, and number of payments. It appears once every required field has a valid value.

Worked examples

Example 1. Inputs:

  • Loan amount: 10,000
  • Annual interest rate: 8%
  • Loan term: 2 years
  • Payments per year: 4

Results:

  • Payment per period: $1,365.10
  • Total paid: $10,920.78
  • Total interest: $920.78
  • Number of payments: 8

How this is worked out: Quarterly payments. r = 0.08 / 4 = 0.02 and n = 2 x 4 = 8. F = (1.02)^8 = 1.1716594. PMT = P r F / (F - 1) = 10000 x 0.02 x 1.1716594 / 0.1716594 = 200 x 6.82549 = 1365.098, shown as 1365.10. Total paid = 1365.098 x 8 = 10920.78. Interest = 10920.78 - 10000 = 920.78.

Example 2. Inputs:

  • Loan amount: 12,000
  • Annual interest rate: 0%
  • Loan term: 1 year
  • Payments per year: 12

Results:

  • Payment per period: $1,000.00
  • Total paid: $12,000.00
  • Total interest: $0.00
  • Number of payments: 12

How this is worked out: Edge case, rate 0. No interest, so payment = principal / periods = 12000 / 12 = 1000. Total paid = 1000 x 12 = 12000. Interest = 12000 - 12000 = 0.

Example 3. Inputs:

  • Loan amount: 200,000
  • Annual interest rate: 6%
  • Loan term: 30 years
  • Payments per year: 12

Results:

  • Payment per period: $1,199.10
  • Total paid: $431,676.38
  • Total interest: $231,676.38
  • Number of payments: 360

How this is worked out: Level payment formula: payment = P x r x F / (F - 1), where r = 6 / 100 / 12 = 0.005, n = 30 x 12 = 360 and F = (1.005)^360. ln(1.005) = 0.00498754, times 360 = 1.7955149, so F = e^1.7955149 = 6.022575. Payment = 200000 x 0.005 x 6.022575 / 5.022575 = 1000 x 1.199101 = 1199.10 to the cent. Number of payments = 30 x 12 = 360.

Example 4. Inputs:

  • Loan amount: 1,000
  • Annual interest rate: 10%
  • Loan term: 1 year
  • Payments per year: 1

Results:

  • Payment per period: $1,100.00
  • Total paid: $1,100.00
  • Total interest: $100.00
  • Number of payments: 1

How this is worked out: One yearly payment, n = 1 x 1 = 1, r = 10 / 100 / 1 = 0.1. Payment = P x r x (1 + r) / ((1 + r) - 1) = 1000 x 0.1 x 1.1 / 0.1 = 1100, which is the loan plus one year of interest. Total paid = 1100. Total interest = 1100 - 1000 = 100.

Where this comes from

A loan repaid by equal payments. payment = P x r x (1 + r)^n / ((1 + r)^n - 1), where P is the amount borrowed, r is the annual rate divided by the payments in a year, as a decimal, and n is the number of payments. At a rate of 0 the payment is P / n. Source: The level-payment (annuity) loan formula, as given in any text on the mathematics of finance: the present value of n equal payments at rate r per period equals the amount borrowed.

Limitations

  • Assumes one fixed rate and equal payments for the whole loan, with no extra payments, fees or balloon payment.
  • Amounts are not rounded to the cent, so a lender's schedule can differ by a few cents.
  • When the term in years times the payments per year is not a whole number, the result includes a part payment.

FAQs

Q: How is the payment worked out?
A: With the standard level-payment formula: payment = P x r x (1 + r)^n / ((1 + r)^n - 1). P is the loan amount, r is the annual rate divided by the payments per year, as a decimal, and n is the number of payments. Each payment covers that period's interest and repays part of the amount borrowed.
Q: What does payments per year change?
A: It sets how often a payment is made. The annual rate is divided by the payments per year, and the term in years is multiplied by it to get the number of payments.
Q: How are total paid and total interest worked out?
A: Total paid is the payment multiplied by the number of payments. Total interest is total paid minus the loan amount.
Q: What happens if the rate is 0?
A: The loan amount is split evenly across the payments, and the total interest is 0.
Q: Why is a payoff time not a whole number?
A: When the payment is given and the time is worked out, the last payment is usually a part payment, so the time is rarely a whole number of periods. The number of payments is that figure rounded up to a whole payment.
Q: What happens if the payment does not cover the interest?
A: The balance would keep growing, so the loan is never repaid. A message is shown in place of a result.
Q: Does it include taxes, insurance or fees?
A: No. It covers principal and interest only. Property tax, insurance and loan fees are not added.

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