Compound interest in the context of "E (mathematical constant)"

An interest rate is the amount of interest due per period, as a proportion of the amount lent, deposited, or borrowed. Interest rate periods are ordinarily a year and are often annualized when not. Alongside interest rates, three other variables determine total interest: principal sum, compounding frequency, and length of time.

Interest rates reflect a borrower's willingness to pay for money now over money in the future. In debt financing, companies borrow capital from a bank, in the expectation that the borrowed capital may be used to generate a return on investment greater than the interest rates. Failure of a borrower to continue paying interest is an example of default, which may be followed by bankruptcy proceedings. Collateral is sometimes given in the event of default.

The doubling time is the time it takes for a population to double in size/value. It is applied to population growth, inflation, resource extraction, consumption of goods, compound interest, the volume of malignant tumours, and many other things that tend to grow over time. When the relative growth rate (not the absolute growth rate) is constant, the quantity undergoes exponential growth and has a constant doubling time or period, which can be calculated directly from the growth rate.

This time can be calculated by dividing the natural logarithm of 2 by the exponent of growth, or approximated by dividing 70 by the percentage growth rate (more roughly but roundly, dividing 72; see the rule of 72 for details and derivations of this formula).

A savings account is a bank account at a retail bank. Common features include a limited number of withdrawals, a lack of cheque and linked debit card facilities, limited transfer options and the inability to be overdrawn. Traditionally, transactions on savings accounts were widely recorded in a passbook, and were sometimes called passbook savings accounts, and bank statements were not provided; however, currently such transactions are commonly recorded electronically and accessible online.

People deposit funds in savings account for a variety of reasons, including a safe place to hold their cash. Savings accounts normally pay interest as well: almost all of them accrue compound interest over time. Several countries require savings accounts to be protected by deposit insurance and some countries provide a government guarantee for at least a portion of the account balance.

The number e is a mathematical constant, approximately equal to 2.71828, that is the base of the natural logarithm and exponential function. It is sometimes called Euler's number, after the Swiss mathematician Leonhard Euler, though this can invite confusion with Euler numbers, or with Euler's constant, a different constant typically denoted ${\displaystyle \gamma }$. Alternatively, e can be called Napier's constant after John Napier. The Swiss mathematician Jacob Bernoulli discovered the constant while studying compound interest.

The number e is of great importance in mathematics, alongside 0, 1, π, and i. All five appear in one formulation of Euler's identity ${\displaystyle e^{i\pi }+1=0}$ and play important and recurring roles across mathematics. Like the constant π, e is irrational, meaning that it cannot be represented as a ratio of integers. Moreover, it is transcendental, meaning that it is not a root of any non-zero polynomial with rational coefficients. To 30 decimal places, the value of e is:

A dividend reinvestment program or dividend reinvestment plan (DRIP) is an equity investment option offered directly from the underlying company. The investor does not receive dividends directly as cash; instead, the investor's dividends are directly reinvested in the underlying equity. The investor must still pay tax annually on his or her dividend income, whether it is received as cash or reinvested.

DRIPs allow the investment return from dividends to be immediately invested for the purpose of price appreciation and compounding, without incurring brokerage fees or waiting to accumulate enough cash for a full share of stock. Some DRIPs are free of charge for participants, while others do charge fees and/or proportional commissions.

In finance, the rule of 72, the rule of 70 and the rule of 69.3 are methods for estimating an investment's doubling time. The rule number (e.g., 72) is divided by the interest percentage per period (usually years) to obtain the approximate number of periods required for doubling. Although scientific calculators and spreadsheet programs have functions to find the accurate doubling time, the rules are useful for mental calculations and when only a basic calculator is available.

These rules apply to exponential growth and are therefore used for compound interest as opposed to simple interest calculations. They can also be used for decay to obtain a halving time. The choice of number is mostly a matter of preference: 69 is more accurate for continuous compounding, while 72 works well in common interest situations and is more easily divisible.

Future value is the value of a current sum of money or stream of cash flows at a specified date in the future, given an assumed rate of return or interest rate. It reflects the time value of money, which holds that a sum of money has different value at different points in time because it can earn a return if invested.

In finance and economics, future value is used to express how much a present present amount will grow when it earns simple interest or compound interest, and to compare different investment or borrowing options.