Understanding Compound Interest

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Learning the concept of compound interest is important to achieving financial goals. Retirement planning, as well as investment scenarios, often depends on calculations involving the compounding of interest. It's also important to become skilled at this concept while you're still young, because as you'll soon find out, time plays a big factor in these calculations too.

In this publication, we're going to cover the topic of compound interest. As part of that discussion, we'll first explain what it is, and why it's such a powerful investment concept. Next, we'll provide equations that demonstrate the calculation of compound interest including formulas that are available in spreadsheet tools such as Excel. Finally, we'll run through some examples demonstrating how the concept is used to solve everyday problems, as well as tell you where you can find an online calculator.

Compound Interest

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Compounding of interest occurs once interest is added to the principal of an investment. From that point forward, not only does the original principal earn interest, but the interest already received also earns interest. The fact that interest received earns additional interest, makes compounding such an important concept for investors. Let's see how this works with a quick example.

Let's imagine we were able to invest $2,000 and earn 10% each year on that investment. A 21 year-old that put this $2,000 away until age 65 would have over $132,000 to spend in retirement. A 50 year-old individual investing that same $2,000 until age 65 would only have around $8,300 to spend in retirement.

The above example demonstrates the two points mentioned earlier. Compound interest is an important investment concept to learn, and it's even more powerful when you have a lot of time on your side. That's because the dimension of time plays a very important role in this calculation.

Compound Interest Formula

The most common calculation performed by financial planners when analyzing the impact of compound interest on an investment involves four factors: the future value of the investment, the present value of the investment, the rate of interest earned in each period, and the number of periods. By knowing these four components, you can use the formula below to perform daily, monthly, and annual compound interest calculations. The formula for compound interest is normally expressed as:

FV = PV x (1 +i) ^ N

where:

FV = future value of the investment
PV = present value of the investment
i = rate of interest earned each period
N = number of periods

Excel and Compound Interest

Using Microsoft Excel, it's also possible to perform compound interest calculations. The function used in Excel is FV (future value). This function is quite flexible, and the syntax used in Excel is as follows:

=FV(rate,nper,pmt,pv,type)

where:

rate = the interest rate per period
nper = the number of payment periods
pmt = used if an additional payment is made each period (otherwise left blank)
pv = the present value of the investment
type (optional) = the number 0 or 1, and is used if additional payments are made whereby 0 = at the end of the period, and 1 = at the beginning of the period

Now that we've seen the two equations used to calculate compound interest, let's put each equation to work using a series of examples.

Compound Interest Examples

In the examples below we're going to demonstrate three concepts. The first has to do with using the compound interest formula to solve a problem that involves annual interest rates. The second problem will demonstrate the formula at work in a calculation that involves monthly compounding. Finally, we'll show how to set up the FV function in Excel to solve a problem.

Example 1 - Annual Interest Rates

In this first example, we're going to revisit the quick example we gave earlier in this publication. As a reminder, we had a 21 year-old that invested $2,000 at 10% and we wanted to value that investment at age 65.

In this problem, we use the following factors in our formula to solve for the investment's future value:

FV = PV x (1 +i) ^ N

where:

FV = future value of the investment
PV = present value of the investment = $2,000
i = rate of interest earned each period = 10% per year or 0.10
N = number of periods = 65 - 21 or 44 years

FV = $2,000 x (1 + 0.10)^44 or

FV = $2,000 x (1.10)^44 or

FV = $2,000 x 66.2640 = $132,528

Example 2 - Monthly Interest Rates

In this second example, we're going to expand our prior example to include monthly compounding of interest, not annual. Once you understand how this monthly example works, then you can compound weekly or daily. The concept is exactly the same except the time period will vary. Once again, we have a 21 year-old that invested $2,000 at 10% compounded monthly, and we wanted to value that investment at age 65.

In this problem, we use the following factors in our formula to solve for the investment's future value:

FV = PV x (1 +i) ^ N

where:

FV = future value of the investment
PV = present value of the investment = $2,000
i = rate of interest earned each period = 10% per year, compounded monthly
N = number of periods = 65 - 21 or 44 years x 12 months

FV = $2,000 x (1 + 0.10 / 12)^44*12 or

FV = $2,000 x (1.00833)^528 or

FV = $2,000 x 79.9793 = $159,959

When compounding monthly, we took the annual value and divided it by 12 (months) to get a monthly interest rate of 0.833% or 0.00833. Then we adjusted the number of periods to 44 years x 12 months = 528 months. The key to solving this problem is having a monthly interest rate and the number of periods also stated as months. This same method can be used to calculate daily or weekly compounding.

You may have also noticed that the monthly compounding result of $159,959 was higher than the annual result of $132,528. That's because a 10% rate of interest that compounds monthly is adding interest to the principal each month, and because we're earning interest on the interest during each compounding interval (month), the future value of the investment will be higher.

Example 3 - Monthly Interest Rates Excel Formula

In this last example, we're going to use Example 2 above, and demonstrate how that problem would be solved in Excel. As a reminder, the syntax is as follows:

=FV(rate,nper,pmt,pv,type)

where:

rate = the interest rate per period = 0.10 / 12
nper = the number of payment periods = 44*12
pmt = used if an additional payment is made each period, otherwise left blank
pv = the present value of the investment = $2,000
type (optional) = the number 0 or 1, and is used if additional payments are made whereby 0 = at the end of the period, and 1 = at the beginning of the period

=FV(0.10/12,44*12,,2000)

= $159,959

You'll note that we left pmt = blank because we were not adding payments to our original investment of $2,000. We also omitted "type" because we weren't making additional payments. Of course, the answer we'd find in Excel is exactly the same as Example 2.

Online Compound Interest Calculator

As promised at the start of this publication, we're going to provide you with a link to our online compound interest calculator. The calculator only needs three inputs: investment, interest rate, and duration. The calculator results include the effective compound interest rates as well as the future values of the investment with compounding. The calculator provides daily, weekly, monthly, quarterly, semi-annual as well as annual values for each of these measures.

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