How this calculator works
A student loan repayment is an instalment loan: the balance falls with each payment by the amount left after interest is charged. In payment mode the calculator holds the term fixed and solves for the level payment. In term mode it holds the payment fixed and solves for the number of months needed. The second mode is the useful one when you are deciding whether to overpay: a payment only slightly above the monthly interest takes a very long time to clear the balance, and a payment at or below the interest never clears it at all. The model assumes a constant rate, no fees and no periods of deferment or forbearance.
Formula
Monthly rate i = annual rate / 12. Payment = P x i / (1 - (1 + i)^-n) for a term of n months. For a fixed payment A, months = -ln(1 - P x i / A) / ln(1 + i), where A must exceed P x i. At a 0% rate, payment = P / n and months = P / A. Total paid = payment x months and interest = total paid - P.
Worked example
A $30,000 balance at 6.5% over 120 months has a monthly payment of $340.64. Total payments are $40,877.27 and interest is $10,877.27, which is 26.61% of the amount paid. Holding the payment at $340 over the same loan instead gives months of -ln(1 - 30,000 x 0.0054167 / 340) / ln(1 + 0.0054167) = 120.32 months.
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Frequently asked questions
Does this include income-driven repayment?
No. This is a fixed-payment amortisation. Income-driven plans set the payment from income and family size and can end in forgiveness; use the student loan forgiveness calculator for that kind of projection.
Why does a small extra payment help so much?
Every dollar above the interest charge goes straight to principal, which reduces future interest. Near the end of a long term the effect is smaller, but early on it can shorten the loan by months.
Should I compare the rate with the APR?
The APR includes fees and is the better comparison between offers. This calculator uses the interest rate you enter, so add any fees to the balance or use the APR if you want the all-in cost.
What happens during deferment?
Interest may continue to accrue, and on unsubsidised loans it is added to the balance when repayment resumes. That capitalisation raises the amount you repay, which this model does not simulate.