If you’re interested in compound interest to maximize personal wealth, you should understand the basic compound interest formulas. While there’s no need to be a mathematician, and you can use a feature-rich compound interest calculator or have an investment professional doing all number-crunching for you, it is still essential to understand the three basic compounding formulas.
All are discussed and explained below. Don’t worry about memorizing them. Instead, try to grasp how the examples work and then try a few of your own hypothetical situations. The first is called the “Rule of 72,” and it’s been around for centuries.
The others are related to how money grows in one-time-investment accounts and in annuities, where you make regular deposits. Here’s how the math works, along with a few examples.
1. Learn the Rule of 72
Ever since moneylenders have been holding wealth on deposit for customers, which goes back at least 2,000 years, the rule of 72 has been used to calculate the amount of time it takes for a deposited sum to double in value at a given interest rate.
The math is amazingly simple. You divide the number 72 by the interest rate. The result is the approximate number of years it will take for the one-time invested amount to double in value.
For example, say you put $10,000 into a bank certificate that pays six percent interest per year. When will you have twice the original amount, namely $20,000?
Divide 72 by the interest rate percentage, which is six, and you discover that it will take your $10,000 about 12 years to double at that rate. Remember two things about the rule.
First, it’s not exact. Second, it delivers wildly inaccurate results with extremely high interest rates. But, it’s a good rule-of-thumb you can use to figure out how your investments will fare, just by doing some simple math in your head.
2. Basics of the Compound Interest Formula
How much will a given sum grow to in a set number of years, assuming a fixed rate of interest? That’s the fundamental question people have when they plunk down a one-time investment into a bank CD or any other kind of interest-bearing account.
The math formula to find the “future value” of the deposit looks like this:
Future Value = Present Value x (1 + interest rate)^N, with the last bracketed value raised to the power of the number of periods (N) the investment grows. It may sound confusing, but it will make sense with an example.
Say you inherit $50,000 and deposit it into a certificate of deposit that pays five percent interest. We’ll ignore tax ramifications for this example because we’re just focused on the basic math calculation.
Also, we’ll assume that you’re planning to leave the money in the CD for four years. So, how much will be in your account at the end of the four-year period, given all those facts?
The calculation looks like this. Future Value = Present Value ($50,000) x (1 + .05)^4 (to the fourth power). Note that we used “.05” to represent the five percent interest rate in decimal form and used the “fourth power” because of the four years the account will grow.
The result is: $50,000 x 1.215, or, $60,775.
3. Basics of the Annuity Formula
Annuities are a bit more complex but not too challenging if you follow the rules. An annuity is a periodic payment or deposit you make. Let’s keep the formula and the example as simple as possible to grasp the key concepts.
The formula answers the question of, “How much will my periodic investment grow to after a certain amount of time at a fixed rate of interest?” The formula looks like this:
Future Value = Periodic payment x ([1+i]^N – 1)/i
In the formula, i is the interest rate, N is the number of periods, and the periodic payment is the set amount you put into the account each period.
Example: Assume you put $1,000 into a bank CD on January 1 every year for five years. The CD pays four percent interest annually. Your formula would look like this:
$1,000 x ([1+.04]^5 – 1)/.04, which comes out to be $5,416.32, which is much more than the simple total of the five, $1,000 deposits. Due to the compound interest effect, you earned an additional $416.32 on your investment.
Common Mistakes
Be careful always to use the correct interest rate in decimal format. For example, five percent is written as .05 when making calculations. Also, note whether you’re calculating a lump sum that grows over time or a series of periodic payments. The results are very different, so be aware of which formula to use.