## Understanding the Benefits of Compounding

This calculator can be used model and view the effects of compounding on both interest rates and the growth of a retirement portfolio. The calculator needs a total of six inputs, including:

- The value of any initial investment, which can also be zero. For example, this value could be the balance in an existing retirement portfolio
- A monthly contribution value into the investment portfolio. Once again, this value can also be zero
- The length of time (in years) over which the monthly contribution will take place
- The expected interest rate earned on all of the money in the portfolio. This includes the initial investment and the monthly contributions
- The possible variance in the interest rate over time. More on how this feature works later on
- Finally, whether the compounding should be annually, semi-annually, quarterly, monthly, weekly, or daily

The calculator then provides the user with seven outputs, including:

- The effective rate of interest on the investments, which is the compound rate of interest
- The total of all monthly contributions made over the length of time selected
- The interest earned over the length of time selected on both the monthly contribution and the initial investment
- Using the value for the interest rate variance, the calculator provides the future value of the investment plus upper and lower range values
- Finally, the calculator provides a five-point graph depicting the value of the investment over time

### What is Compound Interest?

Before we can understand why compounding is important, let’s first step back and define compound interest. The best way to explain this concept is by using an example of a savings account deposit at a bank. In this example, Bank A pays 10% interest on a deposit of 1,000 with compounding quarterly. Bank B pays 10% interest on a deposit of 1,000 with no compounding. Let’s see what the account holder has at the end of one year.

#### Bank A (10% Interest, Quarterly Compounding)

Initial Deposit = 1,000

After 1 Quarter = 1,000 + 25 = 1,025.0

After 2 Quarters = 1,025 + 25.6 = 1,050.6

After 3 Quarters = 1,050 + 26.3 = 1,076.3

After 4 Quarters = 1,076.3 + 26.9 = 1,103.2

#### Bank B (10% Interest, No Compounding)

Initial Deposit = 1,000

After 1 Quarter = 1,000 + 25 = 1,025

After 2 Quarters = 1,025+ 25 = 1,050

After 3 Quarters = 1,050 + 25 =1,075

After 4 Quarters = 1,075 + 25 = 1,100

The above example demonstrates the “power” of compounding, even over the relatively short timeframe of one year.

### Compound Interest Definition

In simple terms, compound interest is interest you earn on interest. With a savings account that earns compound interest, you earn interest on the initial principal plus interest on the interest that accumulates over time. Compounding means more frequent interest earned on interest, which can lead to considerably larger gains when the duration of the investment is longer and when interest rates are higher. In fact, the degree of compounding is a function of frequency and duration. As each of these increases, so does the effect of compounding.

### Interpreting the Results of Our Calculator

One of the nice features of this calculator is the ability to understand what happens if the modeled interest rate varies from your prediction. For example, the default Interest Rate is 6.000%. But what happens if the investment does not provide a 6.000% return? In fact, unless the 6.000% is guaranteed, it is almost certain the actual rate of interest will vary from this value. To model these scenarios, we provide an Interest Rate Variance input for the calculator. With the default rate of 1.500%, the calculator can provide three potential future values of the investment. The Future Value is modeled at 6.000%, while the Upper Range is modeled at 6.000% + 1.500%, or 7.500%. Finally, the Lower Range is modeled at 6.000% – 1.500%, or 4.500%. By providing this information, you can see a possible range of future values.