# Calculating Compound Interest on Investments

Learn the compound interest formula. The compound interest formula determines the future value of an investment after a certain number of years.

The formula itself looks like this: FV=P(1+ic)n∗cFV=P(1+{\frac {i}{c}})^{{n*c}} The variables in the equation are defined as follows:

- “FV” is the future value. This is the result of the calculation.
- “P” is your main.
- “i” represents the annual interest rate.
- “c” represents the interest rate (how many times interest is compounded each year).
- “n” represents the number of years measured.

Gather the variables for the compound interest formula. If interest is compounded more frequently than once a year, manually calculating the formula is difficult.

You can use the compound interest formula for any calculation. To use the formula, you must collect the following information:

Table of Contents

## Determine the principal amount of the investment.

This is the amount of your initial investment.

This could be the amount you deposited into your account or the original value of the bonus.

For example, let’s say the funds in your investment account are $5,000.

Find the interest rate on the debt. The interest rate must be an annual amount expressed as a percentage of the principal amount. For example, an interest rate of 3.45% on the principal value of $5,000.

When calculating the interest rate, you must enter it as a decimal fraction. Convert this by dividing the interest rate by 100.

In this example it would be 3.45%/100 = 0.0345.

You should also be aware of how often debt accumulates. As a rule, interest is calculated annually, monthly or daily. For example, imagine that you charge complex amounts monthly. This means that your interest rate (“c”) will be entered as 12.

Define the period of time you want to measure. This could be a target year for growth, such as 5 or 10 years, or the maturity of a bond.

The maturity date of a bond is the date by which the principal amount of the debt must be paid. For example, we used 2 years, so enter 2.

Use a formula. Enter your variables in the correct places. Please check again to make sure you are entering them correctly. In particular, make sure that your interest rate is in decimal form and that you have used the correct number for the “c” (compound frequency).

An example investment would be entered as follows: FV = $5,000 (1 + 0.034512) 2 * 12 FV = \ $5,000 (1 + {\frac {0.0345}{12))) ^{{2*12 }}

Calculate the exponential part and formula part in parentheses separately. This is a mathematical concept called the order of operations. You can learn more about the concept using this link: Applying Order of Operations.

## Complete the math in the formula.

Simplify the problem by first solving the parenthesized parts of the equation, starting with the fraction.[8]

First, divide the fraction in parentheses. The result should be: FV=5000$(1+0.00288)2∗12FV=\$5000(1+0.00288)^{{2*12}}

Add numbers in brackets.

The result should be: FV=$5000(1.00288)2∗12FV=\$5000(1.00288)^{{2*12}}

Solve the multiplication inside the exponent (the last part above the closing bracket). The result should look like this: FV=$5000(1.00288)24FV=\$5000(1.00288)^{{24}}

Raise the number in brackets to a power.

This can be done on the calculator by first entering the value in brackets (1.00288 in the example), pressing the xyx^{y} button, then entering the exponent (in this case 24) and pressing the enter key.

Example result: FV=$5000(1.0715)FV=\$5000(1.0715)

Finally, multiply the principal by the number in brackets. The result in the example is 5000 * 1.0715 or $5357.50. This is the value of the account at the end of 2 years.

## Subtract the main point from your answer.

This will give you the amount of interest earned.

Subtract the principal amount of $5,000 from the future value of $5,357.50 to get $5,357.50-$5,000, or $357.50.

You will earn $357.50 in interest over 2 years.