• Finance ,
• 11 May

Compound Interest is how you determine the future value of an investment that earns consistent interest over a certain number of years. You can think of this like your savings account at a credit union. The concept of compounding interest is very important in helping you reach your financial goals.

The interest compounds because the interest earned in the first period then earns interest in the second period along with the original investment.  It is the interest earning interest where the word compounding comes from. This concept is important for understanding the basics of the time value of money.

This cycle of interest earning interest shows us why it’s important to save money now. The time dimension of compounding interest tells us that the longer our time horizon, the exponentially more money the investment will earn.

Here is an example of what it looks like in Excel by year.

As you can see on the left we start with the amount colored in peach. At the end of the year, we have a total ending principal balance that shows our original principal balance, plus the compound interest earned. Subtracting the original Principal from our year 3 ending principal gives us our total interest earned over the 3 year period.

While you can do this in a program like Excel, there is a formula we can use. Here we determine the future value by inputting three variables into the equation.

where

Future Value

Present Value

Interest Rate

Number of Years, or Periods.

Future Value

This is what we are trying to calculate. This is the value that we can expect when everything remains constant. As discussed earlier, this is an important building block of understanding how to value investments. If we know we can earn 10% interest and someone asks us if we would rather have 1,000 now or 1,200 at the end of 3 years from now, we know from our example that we can earn more by taking the 1,000 now.

Present Value

This is what the value is of the investment at the beginning.  The first deposit in a savings account for example. You can use this formula for a basic forecast of what your deposit will be after 5, 10, or even 20 years!

Interest Rate

The interest rate is typically provided and we assume it stays constant for our formula. You can take the same example, and play with the interest rate to see how it affects long term growth. You’ll see that the farther out you go in time, the more sensitive your final ending principal balance is to changes in the interest rate.

Number of Years, or Periods.

n is commonly used for the number of years in both finance and statistics. While our example shows years, if you compound monthly, for example, then you can use the same formula. Just be careful about keeping your periods and your rate consistant. You may need to adjust an annual rate down to a monthly rate when compounding monthly for example.