## compound interest formula

### The compound interest formula is used to calculate the final amount of money, known as the future value, when a principal amount is invested or borrowed and it earns interest over a certain period of time

The compound interest formula is used to calculate the final amount of money, known as the future value, when a principal amount is invested or borrowed and it earns interest over a certain period of time.

The formula for compound interest is:

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

Here’s what each symbol represents:

A = the future value or final amount of money.

P = the principal amount, or the initial investment or loan.

r = the annual interest rate (expressed as a decimal).

n = the number of times interest is compounded per year.

t = the number of years.

Let’s break down the formula step by step. Please note that the calculations can be done manually or by using a calculator or spreadsheet:

1. Determine the principal amount (P): This is the initial investment or loan amount.

2. Identify the annual interest rate (r): Convert the stated annual interest rate into a decimal. For example, if the annual interest rate is 5%, you would use 0.05 in the formula.

3. Find the number of times interest is compounded per year (n): This represents how often the interest is added to the principal amount during the year. Common options are annually (1), semi-annually (2), quarterly (4), monthly (12), or daily (365).

4. Determine the number of years (t): This represents the length of time the principal amount will remain invested or the duration of the loan.

5. Calculate (1 + r/n): Add 1 to (r/n). This part of the formula represents the total interest rate per compounding period. For example, if the annual interest rate is 5% and interest is compounded quarterly (n = 4), you would calculate (1 + 0.05/4) = 1.0125.

6. Raise (1 + r/n) to the power of (nt): Multiply the result from step 5 by raising it to the power of (nt). This calculates the total compounding effect over time. For example, if the number of years is 5 and interest is compounded quarterly (n = 4), you would calculate (1.0125)^(4*5) = 1.2824.

7. Multiply P by the result from step 6: Multiply the principal amount (P) by the result from step 6 to calculate the future value (A). For example, if the principal amount is $1,000, you would multiply it by 1.2824 to get a future value of $1,282.40.

So, the compound interest formula allows you to calculate the future value of an investment or loan by considering the initial principal amount, the interest rate, the compounding periods, and the time period.

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