Glossary

Calculator Glossary

Use this glossary to understand the terms that appear across ArithPilot calculators. Each entry explains the idea in plain English, why it matters, a short example, and related calculators where the term is used.

APR

Plain-English definition

APR, or annual percentage rate, is the yearly cost of borrowing expressed as a percentage. It is often used to compare loans and credit products, though the exact fees included can vary by lender and product.

Why it matters

APR helps borrowers compare offers that may have different interest rates, fees, or repayment structures. A lower monthly payment is not always cheaper if the APR, term, or fees are higher.

Example

A loan with a 7% interest rate and large fees may have a higher APR than a loan with a slightly higher interest rate but fewer upfront costs.

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Principal

Plain-English definition

Principal is the starting amount borrowed, invested, or still owed before interest is added. In a loan, it is the balance that repayment gradually reduces.

Why it matters

Principal drives most finance calculations. The same rate applied to a larger principal creates more interest, and extra principal payments can reduce the total interest paid over time.

Example

If you borrow $20,000 and pay $3,000 down, the financed principal may be about $17,000 before taxes or fees.

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Interest

Plain-English definition

Interest is the cost of borrowing money or the amount earned on savings and investments. It is usually calculated from a principal amount, a rate, and a time period.

Why it matters

Interest determines how debt becomes more expensive and how savings can grow. The timing of payments or compounding can change the final total.

Example

$10,000 at 5% simple annual interest earns about $500 in one year before taxes or fees.

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Compound Interest

Plain-English definition

Compound interest means interest is added to the balance, and future interest is calculated on that larger balance. It can apply to savings, investments, and some debt balances.

Why it matters

Compounding makes time an important input. Small differences in rate, contribution timing, or years can produce large differences in long-term results.

Example

$5,000 invested for 15 years can grow much more with monthly contributions than with the starting balance alone.

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Amortization

Plain-English definition

Amortization is the process of paying down a loan through scheduled payments. Each payment usually includes interest plus a principal portion.

Why it matters

An amortization schedule shows why early payments often go mostly toward interest and later payments reduce principal faster.

Example

On a fixed mortgage, the monthly payment may stay the same while the interest portion shrinks as the balance falls.

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Refinance

Plain-English definition

Refinance means replacing an existing loan with a new loan, usually to change the rate, payment, term, or cash-flow profile.

Why it matters

A lower payment is not always a better deal if closing costs are high or the new term extends the debt for many more years.

Example

Refinancing from 7% to 6% may save monthly interest, but the break-even point depends on fees and how long you keep the loan.

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Taxable Income

Plain-English definition

Taxable income is the part of income used in a tax estimate after deductions or adjustments. The exact definition depends on the tax authority and filing rules.

Why it matters

Taxable income is not the same as gross income. Confusing the two can make estimated tax and take-home pay look too high or too low.

Example

If gross income is $80,000 and deductions are $10,000, a simplified estimate may apply the effective rate to $70,000.

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Gross Pay

Plain-English definition

Gross pay is pay before taxes, deductions, benefit costs, or other withholdings. It is often the headline salary or wage amount.

Why it matters

Budgets should usually use after-tax or net pay, not gross pay. Gross pay is still useful for comparing offers and converting salary frequencies.

Example

A $75,000 salary is gross annual pay before payroll taxes, insurance premiums, retirement contributions, or other deductions.

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Net Pay

Plain-English definition

Net pay is the amount left after taxes and deductions. It is often called take-home pay.

Why it matters

Net pay is the number most useful for monthly budgeting because it is closer to what actually reaches a bank account.

Example

If monthly gross pay is $5,000 and estimated taxes and deductions are $1,100, net pay is about $3,900.

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VAT

Plain-English definition

VAT, or value-added tax, is a consumption tax applied to many goods and services in some countries. Prices may be shown with VAT included or before VAT.

Why it matters

Knowing whether VAT is included changes how you calculate the final price or back out the pre-tax amount.

Example

If an item costs 120 with 20% VAT included, the pre-VAT price is 100 and the VAT portion is 20.

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Discount

Plain-English definition

A discount reduces a listed price by a fixed amount or percentage. Sales tax or VAT may be applied before or after discount depending on local rules.

Why it matters

Discounts can make comparisons confusing when one offer uses a percentage and another uses a fixed amount or bundles fees.

Example

A 15% discount on a $200 item reduces the price by $30 before any tax calculation.

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Unit Conversion

Plain-English definition

Unit conversion changes a measurement from one unit to another, such as feet to meters or pounds to kilograms.

Why it matters

A correct number with the wrong unit can still be wrong for the task. Conversions are especially important in measurements, health inputs, materials, and technical work.

Example

10 feet is about 3.048 meters, while 10 meters is about 32.81 feet.

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BMI

Plain-English definition

BMI, or body mass index, compares weight with height using a simple formula. It is a broad screening measure, not a direct body-fat measurement.

Why it matters

BMI can provide quick context, but it does not account for muscle mass, body composition, pregnancy, age-specific interpretation, or individual health history.

Example

An adult who weighs 80 kg and is 180 cm tall has a BMI of about 24.7.

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BMR

Plain-English definition

BMR, or basal metabolic rate, estimates the calories a body uses at rest for basic functions such as breathing and circulation.

Why it matters

BMR is often used as a starting point for calorie estimates, but total daily needs also depend on activity, body composition, health, and goals.

Example

A BMR estimate of 1,700 calories means resting energy use is about 1,700 calories per day before activity adjustments.

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Variance

Plain-English definition

Variance measures how far numbers in a data set tend to be from the mean, using squared differences.

Why it matters

Variance is useful in statistics because it describes spread, but its squared units can be harder to interpret directly than standard deviation.

Example

If values are tightly grouped around the mean, variance is small. If values are widely scattered, variance is larger.

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Standard Deviation

Plain-English definition

Standard deviation measures typical spread around the mean in the same unit as the original data.

Why it matters

It helps compare consistency or variability. A larger standard deviation means values are more spread out from the average.

Example

Test scores with a mean of 80 and standard deviation of 5 are more tightly grouped than scores with the same mean and a standard deviation of 15.

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CIDR

Plain-English definition

CIDR, or Classless Inter-Domain Routing, writes an IP address with a prefix length, such as 192.168.1.10/24.

Why it matters

CIDR notation defines the network size, subnet mask, address range, and usable host count in IPv4 planning.

Example

192.168.1.10/24 belongs to a network with mask 255.255.255.0 and usually 254 usable host addresses.

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