How the arithmetic works

Where figures come from

Every number on this site is transcribed from the authority that published it, is a convention that says it is one, or is something you typed. There is no fourth category. Where something is not known, the page says so rather than filling the space.

Hand-checked rules carry the date a person opened the source and read the figure. Bulk data is labelled differently, because nobody read two thousand institution records by hand and a review date over them would be a lie. Those carry the dataset, the year the figures describe, and the date the script ran.

Capitalization

Two scenarios are computed and compared. In the first, the periods you describe run with capitalization applied where you said it applies. In the second, the same periods run with capitalization switched off everywhere. The difference between the total repaid in each is the cost of capitalizing.

The accrued interest is not the same in both. Once interest joins the principal, every later period accrues on the larger balance, so the counterfactual is walked separately rather than reusing the first walk's figure. Interest sitting outside the principal earns nothing, which is the entire mechanic.

Amortization

A level payment that clears the balance over the term, with interest charged monthly on the outstanding balance. Payments cover interest before principal.

Where a payment does not cover the interest, the shortfall is carried outside the principal rather than added to it, which is how a US federal loan behaves. A schedule that folded it in would overstate every stalled loan. Where the payment can never clear the loan, that is reported as a result rather than raised as an error.

US federal loans accrue simple interest daily on a 365.25-day year. Over an average month that produces exactly the same figure as compounding monthly, so the scheduled payment is identical either way. What differs is the treatment of unpaid interest. Real calendar months are not modelled: a 31-day month accrues more than a 28-day one on a genuinely daily loan, and over a full term those differences cancel to within a few dollars.

Income-driven repayment

The Repayment Assistance Plan applies a bracket rate to the whole adjusted gross income, not to the slice inside the bracket. Fifty dollars a month comes off per dependant and the payment floors at ten dollars.

Income-Based Repayment takes its share of discretionary income, meaning income above 150% of the HHS poverty guideline for the household size, and caps the payment at the ten-year Standard amount.

Projections assume a flat income for the life of the plan. Nobody has one. Because the RAP brackets are cliffs rather than slopes, a career of ordinary raises produces a payment path no calculator can predict from a single income figure.

Canada's Repayment Assistance Plan

Below the published threshold for the household size, nothing. Above it, the payment is capped at the schedule's share of gross family income.

The government publishes both endpoints and says the payment scales gradually between them, without publishing the formula for the middle. So the figure shown above the threshold is a ceiling rather than a bill, and the page says so. Ontario is assessed against its own schedule as well as the federal one, because it has its own.

Public Service Loan Forgiveness

The remaining balance after 120 qualifying payments at the payment you supply. Which months qualify is a rule rather than a calculation, so the plan is an input and the page states the rule. Payments on Tiered Standard earn no credit and the calculator refuses to project on it rather than producing a figure that would be wrong.

Consolidation

The balance-weighted average of the rates, rounded up to the next eighth of one percent. Up, not to the nearest, which is why consolidating always costs at least a little.

Refinancing

Two amortizations, one on the federal terms and one on the private terms, compared on monthly payment and on total repaid. The federal side accrues daily and the private side compounds monthly.

What the comparison cannot price is listed on the page rather than folded into a number. The protections a federal loan carries have no market value that this site could look up, and assigning one would be inventing a figure.

Ordering several loans

Every loan receives its minimum. Whatever the budget has left goes to one loan, chosen either by the highest rate or by the smallest balance. Both are run to the end and the difference is reported. Where the budget is below the combined minimums, the page says so rather than producing a schedule.

Cost of attendance

Annual borrowing accumulates, interest accrues on the running balance from disbursement on an unsubsidized loan, and a grace period is added at the end. Cost and aid are assumed flat, and the programme is assumed to finish on time. All three usually move, so the result is a floor rather than a forecast. Origination fees are not included.

The borrowing bands, which are ours

No government, lender or regulator publishes a threshold for how much student debt is sensible against a salary. The three bands on that calculator are this site's editorial judgement, and they are exported as named constants so they can be found and argued with:

• Under one year's salary. Standard ten-year payments on this much debt take a single-digit share of a gross starting salary.
• One to one and a half years' salary. Payments start to compete with rent. Income-driven repayment becomes worth understanding rather than optional.
• More than one and a half years' salary. Standard payments take a large share of take-home pay. Most borrowers here end up on an income-driven plan for years, which means paying longer and paying more in total.

No band says approved, qualified, eligible or affordable. This site underwrites nobody and has no standing to. A test asserts those words are absent from the band copy, and that test is not a formality.

RESP and the education savings grant

Twenty percent of the first $2,500 contributed each year, plus ten or twenty percent of the first $500 depending on adjusted family net income, capped at $1,000 of grant in any one year and $7,200 over the life of the plan. Unused room carries forward.

Contributions are assumed to arrive through the year, so they earn half a year of return in the year they are made. Provincial top-ups are not modelled.

529 growth

Contributions and compounding, and nothing else. A 529's real value is tax treatment set state by state, and this site has not transcribed those rules, so it does not show them.

Tiered Standard terms

• Under $25,000: 10 years
• Under $50,000: 15 years
• Under $100,000: 20 years
• $100,000 and above: 25 years

What never reaches a URL

Income, adjusted gross income, a balance, a payment, a household size and a salary can be read from a link somebody sends you and can never be written into one. A URL sits in browser history, is logged by every proxy it crosses, and leaks in a referrer header. The list of writable keys is an allowlist and a test asserts the personal ones are not on it.

The privacy page covers the rest.