With the power of compound interest, you can grow your savings faster; however, it can also exponentially increase debts.
It’s been said that mathematical genius Albert Einstein once described compound interest as, “the eighth wonder of the world.” Einstein further stated, “He who understands it, earns it… he who doesn't… pays it.”
So, what is compound interest?
Let’s start first with a definition of interest.
Defining interest
Interest is money paid by (or charged to) people in exchange for borrowing money. A lender will earn interest on the money they loan, and a borrower will pay interest on the money they borrow, such as from a loan or credit cards.
On the other side of the coin, a person who saves or invests their money with a financial institution can also earn interest on the funds they deposit with that bank.
How does simple interest work?
To calculate simple interest, take the principal amount and multiply it by the annual interest rate and the loan term. For example, if you took out a $2,000 loan with a loan term of two years and a 5% interest rate, you’d pay $200 in interest. See below:
$2,000 (principal amount) x 0.05 (interest rate) x 2 (loan term in number of years) = $200
The total amount you’d pay on the loan would be $2,200.
$2,200 = $2,000 (principal amount) + $200 (total interest)
Defining compound interest
Compound interest is interest earned on interest. Depending on the type of account, interest can accrue daily, monthly, quarterly, semi-annually, or annually on the amount that a person originally invests (called the principal) and on previously credited interest.
Over time, compound interest puts the money that people save on steroids.
“People should know that compound interest makes money grow faster. It allows you to build interest on your interest, whereas simple interest is just based on the principal,” says Micha Bender, personal financial literacy coordinator for the New Jersey Department of Education.
The magic of compound interest
Most people don’t become wealthy from their paychecks alone. They do so with a combination of earnings, regular savings, and compounding interest over time. Stated another way: Their money makes money. Compound interest packs a saver’s principal with power.
“Over time, as more interest adds to the original investment, earnings may seem to magically increase,” says Laura Hendrix, Ph.D., an associate professor for personal finance and consumer economics with the University of Arkansas Cooperative Extension Service. “That’s why you may sometimes hear it referred to the ‘magic of compounding.’”
Compound interest formula
With simple interest, if you had an initial amount of $1,000 in a high-yield savings account, and it earned 2% interest annually, at the end of the first year you’d have $1,020. But what would happen if that same initial investment earned compound interest over five years? What would its future value be?
To calculate compound interest, use the following formula:
A = P x (1+ r/n)nt
- A = Principal amount plus interest
- P = Principal amount
- r = Annual interest rate
- t = Time in decimal years
- n = Number of compounding periods per unit of time
With compound interest, you earn interest on your interest. At the end of the fifth year, you’d have $1,104.08.
A= 1,000 x (1 + .02/1)(1)(5)
- P= $1,000
- r = 2% ( .02 as a decimal)
- n = 1 year
- t = 5 years
To break it down a bit more simply, follow the steps in the below image for calculating compound interest:
Stated even more simply: Money + Time + Compound Interest = MAGIC!
Small, regular savings deposits can grow to five-, six-, and even seven-figure sums. The amount of money you save is less important than having a regular saving habit. As your bank account balance grows, you earn interest on increasingly larger sums.
A good analogy for compound interest can be seen in the television show, “Who Wants to Be a Millionaire?” Prizes for contestants build up slowly at first, much like compound interest on small dollar amounts during the early years of saving. Later, game show prizes double to higher amounts, just like someone who has been in the saving game for a while earning compound interest.
Some compound interest math
“Compound interest is the foundation for building savings over the long term,” says Jesse Ketterman, Ph.D., an extension educator and accredited financial counselor with the University of Maryland. “It can help you by reinvesting the interest you earned on your savings.”
The good news about compound interest is that its awesome magical power works for everyone regardless of income, occupation, and education. If you set aside any amount of money into a savings or investment account, compound interest can be your BFF.
To prove this point, below are actual numbers that assume a 6% average annual rate of return with six different amounts of weekly savings ranging from $5 to $100. The table shows how much savings you can achieve by age 65 if you have compound interest on your side.
| Age | $5/Week | $10/Week | $25/Week | $50/Week | $75/Week | $100/Week |
| 25 | $ 43,149 | $ 86,298 | $ 215,745 | $ 431,490 | $ 647,234 | $ 862,979 |
| 30 | $ 30,869 | $ 61,737 | $ 154,344 | $ 308,687 | $ 463,031 | $ 617,374 |
| 35 | $ 21,764 | $ 43,529 | $ 108,822 | $ 217,645 | $ 326,467 | $ 435,290 |
| 40 | $ 15,015 | $ 30,030 | $ 75,074 | $ 150,149 | $ 225,223 | $ 300,297 |
| 45 | $ 10,011 | $ 20,022 | $ 50,054 | $ 100,109 | $ 150,163 | $ 200,218 |
| 50 | $ 6,301 | $ 12,602 | $ 31,505 | $ 63,011 | $ 94,516 | $ 126,021 |
| 55 | $ 3,551 | $ 7,101 | $ 17,754 | $ 35,507 | $ 53,261 | $ 71,014 |
Some noteworthy patterns are evident:
Time is money
The more someone saves each week ($100 vs. $5) and the longer they save (40 years vs. 10 years until age 65), the more money they will accumulate.
Age matters
Note the widening gap between account balances at different ages and dollar amounts.
Baby steps work
Any amount of savings is better than no saving at all and can snowball into a large lump sum. Even saving $5 a week will result in a five-figure sum if you start socking away money at or before age 45.
The flip side of compound interest
Just like compound interest can grow your savings, it can also grow your debt and work against you. This is when compound interest is your worst enemy.
Over time, the cost of interest can be significant. This is especially true for debts that have a long pay-off period (e.g., home mortgages, student loans) or in circ*mstances where you are only making the minimum monthly payments on a large balance, like a credit card debt. When you only pay the minimum amount due each month, it can cause your credit card balance to stretch out for years, even decades.
Example: A $1,000 balance on a credit card with an 18% annual percentage rate (APR) will cost about $684 in interest charges and take eight years to repay if you only make minimum payments (3% of the balance).
“Compound interest is great when you are on the receiving end, but not when you are trying to pay down debt,” Hendrix says. “When interest is added to debt, you could end up paying interest on increasingly larger amounts.”
Five tips to maximize compound interest
No. 1: Save early
Compound interest is not retroactive! In other words, you cannot earn compound interest on money that was not previously saved. The best time to become a first-time saver is when you receive your first paycheck. The second best time is today.
A useful tool to encourage saving is the 30-Day $100 Savings Challenge. After you save your first $100, “rinse and repeat” each month to grow the principal on which you receive interest payments.
No. 2: Save as much as you can
Give compound interest as much “juice” as possible by powering up your savings deposits.
Increased savings may require earning a higher income via a new job, promotion, and/or side hustle. You can also find money to save by trimming expenses or earmarking windfall income sources such as tax refunds and the expanded child tax credit in 2021.
No. 3: Save consistently
Keep adding money to your principal over a long period of time.
A great way to save consistently is automation. Here are two examples:
- Have your employer deduct savings deposits from your paycheck and direct them into a savings account.
- Transfer money from a checking account to a savings account using an app.
No. 4: Save tax-deferred
Compound interest works best in tax-deferred retirement savings accounts such as an individual retirement account (IRA) or 401(k) or 403(b) plan. Earnings are not taxed until withdrawal, typically at retirement.
The longer savings grow free of taxes, the more time compound interest has to work its magic.
No. 5: Pay off debt quickly
“Compound interest is bad when it comes to your debt, because it causes your debt to rise faster,” Bender says.
The secret to paying off debt quickly is to pay more than the minimum monthly payment. This will also save you money on the amount of interest you may owe, and therefore, the potential overall cost of the debt. For example, that $1,000 credit card balance noted above can be repaid in four years at a cost of $285 in interest by doubling payments to 6% of the outstanding balance. This is a savings of $399 from making minimum payments.
Of course, the best-case scenario, if you can afford it, is to pay credit card bills in full each month to avoid accumulated interest.
The bottom line
Many people don’t realize the awesome power of compound interest and their ability to build wealth without winning a lottery or receiving some type of windfall.
As the old saying goes, “Time is money.” Compound interest can be your BFF or your worst enemy. The choice is yours.
Article contributors
Micah Bender is the lead educator for BS Financial Literacy, where he teaches personal financial literacy to college athletes. He is also the personal financial literacy coordinator for the New Jersey Department of Education.
Laura Hendrix, Ph.D., is an associate professor for personal finance and consumer economics with the University of Arkansas Cooperative Extension Service. She has more than 20 years of experience in personal finance education and is an Accredited Financial Counselor.
