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Student Loan Payoff Calculator

Calculate how long it will take to pay off a student loan at a fixed monthly payment, and how much interest you will pay along the way.

What this tool does

Calculate how long it will take to pay off a student loan at a fixed monthly payment, and how much interest you will pay along the way. You fill in these fields: Loan amount, Annual interest rate, and Monthly payment. It shows number of payments, time to pay off, total interest, and total paid.

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.
  • Monthly payment: A number. Must be greater than 0. The same amount paid every period. Principal and interest only: leave out taxes and insurance.

How to use

  1. Enter the loan amount.
  2. Enter the annual interest rate as a percentage.
  3. Enter the monthly payment.
  4. Read the result: number of payments, time to pay off, total interest, and total paid. It appears once every required field has a valid value.

Worked examples

Example 1. Inputs:

  • Loan amount: 1,000
  • Annual interest rate: 12%
  • Monthly payment: 88.85

Results:

  • Number of payments: 12
  • Time to pay off: 1.00 years
  • Total interest: $66.18
  • Total paid: $1,066.18

How this is worked out: Monthly payments, a textbook case. r = 0.12 / 12 = 0.01 and n = 12. F = (1.01)^12 = 1.12682503. PMT = 1000 x 0.01 x 1.12682503 / 0.12682503 = 88.8488, shown as 88.85. Total paid = 88.8488 x 12 = 1066.19. Interest = 1066.19 - 1000 = 66.19.

Example 2. Inputs:

  • Loan amount: 12,000
  • Annual interest rate: 0%
  • Monthly payment: 1,000

Results:

  • Number of payments: 12
  • Time to pay off: 1.00 year
  • Total interest: $0.00
  • Total paid: $12,000.00

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%
  • Monthly payment: 1,199.1

Results:

  • Number of payments: 361
  • Time to pay off: 30.00 years
  • Total interest: $231,677.06
  • Total paid: $431,677.06

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: 12%
  • Monthly payment: 1,010

Results:

  • Number of payments: 1
  • Time to pay off: 0.08 years
  • Total interest: $10.00
  • Total paid: $1,010.00

How this is worked out: Interest for the first month is 1000 x 0.01 = 10, so a payment of 1010 clears the balance in one payment. n = -ln(1 - 1000 x 0.01 / 1010) / ln(1.01) = -ln(1000 / 1010) / ln(1.01) = ln(1.01) / ln(1.01) = 1. Years = 1 / 12 = 0.0833333. Total paid = 1010. Interest = 1010 - 1000 = 10. One month is 1/12 of a year, written here to twelve places.

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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