Student Loan Calculator

The worked example, quantified

The worked example — call it Example A, a fictional $30,000 balance at 5.5% over 10 years — costs $325.58 a month and $9,069 in interest, for $39,069 repaid across 120 payments. Add a fictional $100 a month and the same engine reports the loan paid off 2 yr 10 mo sooner, with $2,753 less interest. Every figure on this page is computed when the page is built by the engine behind the form, on illustrative inputs — not quotes or typical figures.

What the engine computes, step by step

The form hands the balance, rate and term to the engine's schedule function, which runs the steps below in order and returns a typed result or an explicit, human-readable error; when the extra field is greater than zero, the form asks a second engine function for the with-and-without comparison. The interface only formats what comes back; it never does arithmetic of its own.

1. Validation. The balance must be greater than zero, and the rate cannot be negative or exceed the engine's ceiling; a value that fails returns a message in the engine's own words, never NaN or infinity. An extra of zero or less is treated as no extra — the comparison line is simply omitted.
2. Monthly rate. Payments use the standard amortized-loan (PMT) formula with monthly compounding, the convention behind US mortgages and most consumer loans, so the annual rate is divided by twelve: 5.5% ÷ 12 = 0.004583.
3. Number of payments. Years × 12 — 120 for the 10-year option; the five menu terms are 60, 120, 180, 240, 300 payments.
4. The fixed payment. The formula on the balance at the monthly rate over 120 payments gives $325.58, the one payment that carries the balance to zero exactly at the last month. The companion guide derives it.
5. The schedule. The methodology page states the rule: "A fixed monthly payment covers the interest accrued on the balance that month, and the remainder reduces the principal; the schedule is computed one month at a time so extra payments and payoff dates are exact." Each month: interest = balance × (annual rate ÷ 12); the rest of the payment, plus any extra, comes off the balance; repeat until the balance is within a fraction of a cent of zero.
6. The totals and the comparison. Total interest is the sum of the monthly charges and total repaid is the balance plus that interest — $9,069 and $39,069 here. When the extra field is greater than zero, the engine runs the schedule a second time with the extra added to every payment from month one and reports the gap; the scheduled payment is not recomputed.

Month one, and the shape of a ten-year schedule

In month one the balance is the whole $30,000, so interest is $30,000 × 5.5% ÷ 12 = $137.50, and the remaining $188.08 of the $325.58 payment reduces the balance: 42.2% of the first payment is interest. On this balance, rate and term principal exceeds interest from the first payment; the reference loan recomputed below, over thirty years, starts with interest taking 83.4% of the payment. In month two interest falls to $136.64 and principal rises to $188.94; repeated 120 times, that drift clears the balance in the final month.

The first row records $1,592 of interest against $2,315 of principal, and the balance falls below half during year 6. Two identities, re-checked at build time, tie the rows to the totals: the Principal column sums to the balance borrowed, $30,000, and the Interest column to the total-interest line, $9,069. Each month's interest is the balance times the monthly rate, so the charge falls as the balance falls.

The five terms in the menu

To the engine each menu option is only a different number of payments. The table runs the example balance at 5.5% through all five; every cell is an engine output.

Stretching the term from 5 to 25 years lowers the payment from $573.03 to $184.23 and raises total interest from $4,382 to $25,268 — 5.8 times as much — because the balance keeps accruing interest for 240 more months. The engine reports the figures; whether a lower payment for more years fits a budget is not a question the arithmetic answers.

What the extra payment does

The extra-payment field does not change the scheduled payment. It asks the engine to run the schedule twice — without the extra, and with it added to every payment from month one — and to report the gap. In the example the payment stays $325.58, the total paid each month becomes $425.58, and in month one the principal portion rises from $188.08 to $288.08 while the interest charge stays $137.50: the extra reaches the balance that month, and the next month's interest is charged on the smaller figure. The schedule with the extra ends in month 86 instead of month 120, so the result line reads "debt-free 2 yr 10 mo sooner, saving $2,753 in interest". Interest saved is the gap between the two schedules' interest totals — $9,069 and $6,316 — interest one schedule charges and the other never does, not money paid and returned.

Doubling the extra does not double the months or the interest saved — $50 a month saves $1,628, $100 saves $2,753 — because each added dollar meets a schedule already shortened by the dollars before it. The extra is one fixed amount from month one; there is no input for a lump sum, a later start or a changing amount. The engine compares; it does not recommend an amount.

Rate and balance: what moves the payment

The balance scales the result in proportion: a fictional $60,000 at the same rate and term returns $651.16 a month and $18,139 of interest, exactly twice the example — an identity this page checks when it is built. The rate enters through the monthly rate and moves the payment unevenly. The table holds the balance and the 10-year term fixed at fictional rates one percentage point either side of the example's.

One point up adds $15.07 a month and $1,808 of interest over the term; one point down removes $14.66 and $1,760. The two steps are not equal; the companion guide works through that non-linearity.

The reference figure, recomputed

The methodology page names the figure the engine is validated against: a $200,000 loan at 6% over 30 years. Recomputed here when the page is built, the same function the student loan form calls returns a payment of $1,199.10 and total interest of $231,676, matching the methodology page and the automated tests. The engine has no loan-type input; only the balance, rate and term differ.

How to read the result

• The large "/ month" figure is the fixed principal-and-interest payment — $325.58 here. It does not change when an extra is entered.
• Total interest over the term is the sum of every month's interest charge, to whole dollars: $9,069.
• Total repaid is the balance plus that interest, $39,069, not the displayed payment multiplied by 120.
• The extra-payment line appears only when the extra is greater than zero; blank counts as zero and the line is omitted.
• Copy result places a one-line summary on your clipboard: payment, total interest and, with an extra, the interest it saves.

Money is shown to the cent, or to whole dollars for large totals like lifetime interest; internally every calculation keeps the full precision of IEEE-754 double-precision arithmetic, and nothing is rounded between steps. Your lender's figure may differ by a few cents depending on their rounding and day-count conventions — the difference is presentational, not an error.

Where the calculator stops

The limits are the engine's, and the methodology page states them. The calculators model fixed-rate, fully amortizing loans; they do not model adjustable-rate mortgages, interest-only periods, balloon payments, or negative amortization. Whatever rate you enter is held fixed for every month, and the payment is set by the balance, rate and term alone — an arrangement in which the payment is set by anything else is outside the arithmetic. The balance you type is the balance at the first payment: the engine has no input for interest that accrued before that month, and it knows no calendar, so "sooner" is a count of payments, not a date. The term is a menu of five whole-year options — the Loan Calculator accepts any term in years. There are no fee or insurance inputs, and there is one balance at one rate: several loans are several runs of this form, or a job for the Debt Payoff Calculator, which runs a set of balances together through a different engine function.

Inputs are validated before any arithmetic runs. A balance of zero is answered with "The loan amount must be greater than 0." A negative rate with "The interest rate cannot be negative." A rate of 150% with "Enter an interest rate below 100%." And a correct calculation can still be the wrong calculation for your situation — choosing the right loan for a real-world decision is judgment we cannot automate.

Common misreadings

• Reading the extra-payment line as a new payment. The payment does not change; the number of payments does — 86 instead of 120 here.
• Multiplying the displayed payment by the months. Total repaid is $39,069.46; $325.58 × 120 is $39,069.60, and any gap is display rounding.
• Reading the 10-year default as a recommendation. It is the option the menu opens on; the engine attaches no meaning to it beyond 120 payments.

Frequently asked questions

Not financial advice: a general educational estimate. Federal repayment options, IDR formulas, and forgiveness rules change — check current terms with your servicer or studentaid.gov before deciding. Values are processed locally in your browser and never transmitted. See the methodology page.