The interest on a loan or deposit that is calculated using both the initial principal and the accrued interest from previous periods is known as compound interest. It can be thought of as "interest on interest" and, when compounded frequently, can result in a significant increase in the principal's value over time.

Simple interest only considers the initial principal when calculating interest, unlike compound interest. Compound interest is when interest is earned over a period of time and added to the principal so that the interest is calculated on a larger sum the following period. The value of the principal will grow exponentially as a result of the fact that the interest rate will rise over time.

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The amount of interest that is accrued over time can vary significantly depending on how often interest is compounded. For instance, if interest is compounded annually rather than quarterly or even monthly, the total amount of interest earned will be lower.

Compound interest is calculated using the formula A = P(1 + r/n)(nt), where A represents the final sum, P represents the principal, r represents the annual interest rate, n represents the number of times the interest is compounded per unit t (typically a year), and t represents the number of years the investment has been made.

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The interest on a loan or deposit that is calculated using both the initial principal and the accrued interest from previous periods is known as compounding interest. Compound interest is calculated using the following formula:

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

Where:
A = the future value of the investment/loan
P = the principal investment amount (the initial deposit or loan amount)
r = the annual interest rate (decimal form)
n = the number of times that interest is compounded per year
t = the number of years the money is invested or borrowed for

The future value of an investment of $1,000 at 5% annual interest, compounded every year for ten years, would be, for instance:

A = $1000 (1 + 0.05)^10 = $1628.89

In order to account for the fact that interest is also earning interest, compound interest is a method of calculating the interest on an investment or loan. The total amount of interest earned over time increases with the frequency of compounding.

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