Compound Interest

What Is Compound Interest and How Does It Work?

Compound interest is the accumulation of interest associated with a principal balance and previously accrued interest. The latter part of the accumulation is what leads many people to describe compound interest as “interest on interest.”

Mathematically, the compounding effect accelerates the rate at which the value of an investment or debt obligation grows. It is amplified when any of the following situations occur:

• The nominal interest rate (stated rate) is increased.
• The compounding frequency is increased.
• The time until maturity is extended.

Incidentally, compounding frequency refers to the number of times per year that interest is regularly computed and accumulated.

Most banks offer financial instruments that compound daily, monthly, quarterly, semiannually and annually. If you are investing, then compound interest works in your favor by building wealth — but if you have a loan that’s compounding interest, then you are accruing more debt. Compound interest can affect your personal finances depending on how it is used.

Compound Interest vs. Simple Interest

The best way to illustrate compound interest is to contrast it with simple interest. Compound interest grows exponentially, while simple interest grows linearly. In other words, with simple interest, the interest is computed based solely on the principal balance. There is no compounding of previously earned interest. Let’s clarify things with a simple example.

Assume you have the option of depositing $1,000 into either of the following high-yield savings accounts:

1. Account ABC offers 5% annual interest with no compounding (simple interest).
2. Account XYZ offers 5% annual interest compounded annually.

If you go with Account ABC, you will earn $50 of annual interest income ($1,000 × 1.05 = $1,050), and it will not change. However, if you go with Account XYZ, your interest income will grow each year. For the first three years, you can expect the following:

• By the end of the first year, your $1,000 balance will grow to $1,050 ($1,000 × 1.05 = $1,050), yielding $50 of annual interest income.
• By the end of the second year, your balance will grow to $1,102.50 ($1,050 × 1.05 = $1,102.50), yielding $52.50 of annual interest income.
• Then, by the end of the third year, your balance will grow to $1,157.63 ($1,102.50 × 1.05 = $1,157.63), yielding $55.13 of annual interest income.

As illustrated above, the annual interest income for Account XYZ grows continually due to the compounding of previously accrued interest. Essentially, this arrangement gives you an increasingly large base of money to compute future interest. It’s often described as a snowball effect, where a small investment steadily grows bigger and bigger over time, like a snowball rolling down a hill.

How Do You Calculate Compound Interest?

Regardless of the financial instrument, compound interest can be computed easily with the formula below. It computes the interest accumulated over a specified number of years, given the beginning principal, nominal interest rate and compounding schedule.

I = P(1 + rn)^{(n × t)}-P

Key:
I = Compound interest
P = Beginning principal amount
r = Nominal interest rate
n = Number of times interest is compounded per year
t = Time in years

For example, assume you invest $10,000 (P) in a debt instrument offering a 4% nominal rate (r). The time until maturity is 15 years (t), and interest is compounded annually (n). As evidenced below, you will earn $8,009.44 (I) by the time the instrument matures.

I = $10,000 × (1 + 0.04/1)^{(1 × 15)} – $10,000 = $8,009.44

With simple interest, the earnings would only amount to $6,000 ($10,000 × 0.04 × 15 = $6,000). The compounding effect has created over $2,000 of additional value. Incidentally, if the interest were compounded monthly rather than annually, the interest earnings would be even higher, as shown below.

I = $10,000 × (1 + 0.04/12)^{(12 × 15)} – $10,000 = $8,203.02

What Are the Best Compound Interest Investments?

All types of financial instruments offer the prospect of compound interest, but only savings accounts, certificates of deposit, money market accounts and certain fixed-income investments offer guaranteed compounding.

When putting money into these instruments, you should strive to do so as soon as possible – because the longer your time horizon, the greater your money-making potential. Moreover, when selecting an instrument, you should focus on those that offer the highest nominal interest rates and most frequent compounding schedules. This will help you maximize your cumulative earnings.

Can Compound Interest Make You Rich?

When speaking in terms of saving and investing, the power of compound interest is highly accretive to wealth. It can help you make big money in the long term, especially if you start investing early. In fact, a smaller investment early on can help you build more wealth than a bigger investment later.

However, when it comes to borrowing, compound interest has an erosive effect. It causes you to rack up interest charges quicker and can lead to higher levels of debt. Keep this in mind the next time you decide to open a new credit card or other types of revolving line of credit.