What is Compound Interest?

Compound interest is a type of interest calculated on both the original principal of a loan or deposit and the accumulated interest of prior periods. It differs from simple interest, which is calculated just on the principle amount.

Compound interest can be expressed as follows:

A = P(1 + r/n)^(nt)

where:

A is the final amount (principal + interest)

P is the initial principal

r is the annual interest rate

The number n represents the number of times interest is compounded every year.

t is the number of years

For example, if you deposit $1000 in a savings account with an annual interest rate of 5% that compounds interest quarterly, your account balance after 5 years would be:

A = 1000(1 + 0.05/4)^(4*5) = $1276.28

Compound interest can be a powerful tool for growing your savings or paying off a loan, as it allows the interest to compound over time, resulting in a larger final amount. However, it can also work against you if you are borrowing money, as the interest charges can add up quickly.

Compound interest is often used in financial products such as savings accounts, loans, and investment accounts. It is important to understand how compound interest works and to carefully consider the terms of a financial product when making a decision about whether to invest or borrow money.

Consider the following example to demonstrate how the formula works:.

You have $100,000 in two separate savings accounts, each earning 2% interest. The interest in one account is compounded annually, while the interest in the other is compounded daily. After a year, you remove funds from both accounts.

You’ll get the following from the first account, which only accumulates interest once a year:

$100,000 × (1 + (.02 / 1)

1×1 = $102,000

You will receive the following from the second account, which earns interest daily:

$100,000 × (1 + (.02 / 365)365×1 = $102,020.08.

Because the interest you earn each day in the former scenario also earns interest on consecutive days, you earn $20.08 more than the account that accumulates money annually.

Compound interest has a greater long-term impact since it earns interest on higher account balances after years of earning interest on earlier interest earnings. If you left your fund in the account for 30 years, it would look somewhat like this.