Glossary

These are the meanings the calculators on this site use. They are mathematical definitions set by a formula; real product terms or laws may define the same name differently. Each calculator states on screen the definition it used.

Simple interest

Interest is added to the principal only. Interest = principal × annual rate × years. For example, principal 1,000,000, 3% a year, 2 years gives interest 1,000,000 × 0.03 × 2 = 60,000.

Compound interest

Interest earns interest too. If interest is added m times a year, amount = principal × (1 + annual rate ÷ m)^(m × years). For example, principal 1,000,000 at 3% added once a year is 1,030,000 after 1 year and 1,000,000 × 1.03² = 1,060,900 after 2 years.

Nominal annual rate (APR)

On this site this means a rate stated per year, with the number of compounding periods set separately. The same name (APR) may be used in laws or product notices with a different meaning, for example one that includes fees, so please go by the definition shown in each calculator.

Effective annual rate (EAR)

The rate at which money actually grows over one year when interest is compounded m times a year. EAR = (1 + annual rate ÷ m)^m − 1. A 12% rate compounded once a year has an EAR of 12%; compounded twice a year it is (1.06)² − 1 = 12.36%.

Level-payment (equal total payment) repayment

A way of repaying a loan so that the amount paid each period (principal plus interest) is the same. With periodic rate i, n payments and principal P, each payment is P × i ÷ (1 − (1 + i)^(−n)) when i is not zero. Early payments are mostly interest and later ones are mostly principal.

Equal-principal repayment

The same amount of principal is repaid each period, and interest is charged on the principal that remains. Because the remaining principal falls, the payment gets smaller each period.

Interest-only (bullet) repayment

Only interest is paid until maturity, and the principal is repaid in one sum at maturity.

Percent (%) and percentage points (pp)

A percent is a ratio out of 100 (y% of x is x × y ÷ 100). A percentage point is the difference between two percent values. If a rate goes from 3% to 4%, it has risen by 1 percentage point, and by about 33.3% in relative terms (from 3 to 4).

Rounding rules

• Round half up: if the discarded part is exactly one half (0.5), round up. This is the default on this site.
• Round down: drop everything below the digit shown.
• Round up: if anything other than zero lies below the digit shown, go up one unit.
• Round half to even: if the discarded part is exactly one half (0.5), go to the nearest even digit. For example, 2.5 becomes 2 and 3.5 becomes 4.

Depending on the rule, a result can differ by one unit of the currency.

Day-count basis

Actual days counts calendar days as they are. Some notations, such as 30/360, treat a month as 30 days and a year as 360 days. The basis you use changes the interest for the same period slightly, and each calculator here states the basis it used.

Margin and markup

As defined on this site, margin = (price - cost) / price and markup = (price - cost) / cost. With a cost of 80 and a price of 100, the margin is 20% and the markup is 25%. The two words are often mixed up.

Break-even point

The sales quantity at which profit is zero. As defined on this site, break-even quantity = fixed costs / (price - variable cost per unit). With fixed costs of 1,000,000, a price of 10,000 and a variable cost of 6,000, it is 1,000,000 / 4,000 = 250 units.

Present value and future value

Future value is what money today grows to at a given rate; present value is a future amount brought back to today at the same rate. For a single amount, present value = future value / (1 + rate)^periods. The annuity calculator (the same amount every period) adds this up over every period.

Net present value (NPV)

The sum of the cash flows by period (inflows positive, outflows negative), each discounted to today at the discount rate. NPV = sum of cash flow(t) / (1 + rate)^t; this site treats the first cash flow as t = 0. How to read it depends on the situation, so do not decide on an investment from this number alone.

Internal rate of return (IRR)

The per-period rate that makes the NPV zero. There is no closed formula, so it is an approximate value found by iteration; when the cash flows change sign more than once there can be several IRRs or none.

Refinancing

Replacing an existing loan with a new loan on new terms. The refinance comparison calculator works out, under assumed conditions, how much the monthly payment falls and how long it takes to recover fees and other costs (break-even). In practice, the lender's early-repayment fee, screening and contract terms take precedence.

Total monthly housing cost (similar to PITI)

Besides the loan payment (principal and interest), it adds property tax, home insurance, fees such as HOA dues and mortgage insurance. It is a concept similar to the US PITI (principal, interest, taxes, insurance), but the components and tax systems differ, so the two are not identical.

Quartiles

Values that split sorted data into four parts. The first quartile (Q1) is the 25% point, the third quartile (Q3) is the 75% point, and the IQR is Q3 - Q1. Because there are several calculation methods, the statistics calculator lets you choose "inclusive" (the same method as the spreadsheet QUARTILE.INC) or "exclusive" (the same as QUARTILE.EXC).

Pre-tax and after-tax

The amount before tax is taken off is pre-tax; the amount after is after-tax. A calculator that uses a tax rate shows its source and the date we checked.

Maturity

The day the contract period of a product such as a deposit, savings plan or loan ends.