### What is compound interest?

*“ Compound interest is the eighth wonder of the world. He who understands it earns it … he who doesn’t … pays it.” — Albert Einstein *

Compound interest can be thought of as “interest on interest.” This means that when an asset can compound, your investment grows faster than a typical one.

Generally speaking, interest makes an investment, savings, or debt grow. But compound interest takes it one step further. In most cases, your investment will yield simple interest, like 10% of your $1,000 investment for 5 years. That means you only get $500. On the other hand, with compound interest, your $1,000 investment for 5 years at 10% will give you $610.51. This is because the 10% yield is invested back, making your capital bigger.

### Math is fun, especially if it is about your finances

To demonstrate this, let’s imagine Ms. Elsa has $100,000 in a bank. The bank offers 2.5% annual interest to its clients. Presuming she did not withdraw anything from her savings, her money will grow to $102,500 in a year. The next year, assuming that she will touch her savings, the interest will not be based on her original $100,000 savings but on her existing $102,500. Thus, she will have $105,062.50 instead of $105,000. In two years, she gained $62.50 as compound interest.

You can test out potential compound interest with the Compound Interest Calculator made by the federal government at investor.gov.

Most mathematicians use the formula below to calculate compound interest:

A = P (1+r/n)nt

“A” is the total amount of compound interest.

“P” is the principal amount or the initial investment.

“R” is the annual interest rate; it should take the decimal form.

“N” is the number of times the interest is compounded per year.

“T” is the time or the number of years.

Let’s put Ms. Elsa’s case into the equation again. P is $100,000. R is 2.5%. So, it is 0.025 in decimal form. N is “1” because her bank charges interest annually. T is “3” because we will calculate how much compound interest in 3 years. Now, let’s break the equation down.

A = $100,000 (1+0.025/1)(1)(3)

A = $100,000 (1+0.025)3

A = $100,000 (1.025)3

A = $100,000 (1.076890625)

A = $107,689.0625

So after 3 years, Ms. Elsa accumulated $7,689.0625 as compound interest. She earned $62.50 in the first two years, which grew to a whopping $7,626.56. Amazing, right?

All this said, real banks usually have an average interest rate of only 0.01%, and online banks offer around 0.05%. So expect your calculations to be much smaller than you see in these examples.

### Debt compound interest

While compound interest might be a positive force for investors, it can be an insidious enemy for creditors. Financial institutions—especially banks and lending companies—earn a massive amount of cash from interest. Compounding debt interest typically does not come annually. Interest starts kicking in every six months, three months, or even monthly.

To illustrate, let’s use Ms. Elsa again. She took a loan of $20,000 from Hans Lending Corp. at a monthly interest rate of 5%. Unfortunately, she was not able to pay her dues. She promised to settle everything in 2 years. So, the equation goes:

A = $20,000 (1+0.05/12)(12)(2)

A = $20,000 (1+.06)24

A = $20,000 (1.06)24

A = $20,000 (25.44)

A = $508,800

Because of Ms. Elsa’s delinquency, she will pay $508,800 in 2 years. It is as if she is paying $488,800 which she did not even owe.

### Installment Schemes

Aside from banks, insurance, and loan payments, it is also applicable to installment purchases. Let us use Mrs. Elsa as another example. She wants to buy the latest model of the Stark Phone. She cannot afford it at the moment. The saleslady tells her that she can pay via installment with some monthly compound interest. So Ms. Elsa acquires the Stark Phone after paying the down payment. Compound interest, in this case, will be computed after the price of the Stark Phone is deducted from the down payment. The remaining balance will soon be calculated using the compounding interest formula.

### In a nutshell

Compound interest can be your worst enemy—but it can also be your best friend.

Being able to calculate it for a projected term is one sign of financial maturity. If you plan well, you can invest in companies with little to no debt, or even into companies that receive revenue from giving loans with compound interest. Make compound interest your ally, and it can give you a lifetime of profit.