Knowing how interest on savings accounts works can help investors earn as much as possible on the money they save. Let's say you have $1,000 in the bank and the account earns 1% interest. In fact, until around 2019, 1% was far more than what most banks were paying in savings accounts due to historically low interest rates. But with interest rates rising, some banks are offering savings accounts that yield over 2%. For this article—which is all about compound interest and how it works—1% is a good round number to illustrate this type of interest's effects.

Key Takeaways

  • Interest compounded over a long enough time period can add nicely to an emergency fund.
  • Compound interest is interest calculated on principal and earned interest from previous periods; simple interest is only calculated based on principal.  
  • Banks state their savings interest rates as an annual percentage yield (APY), which includes compounding.

Interest on Interest

In the simplest of words, $1,000 at 1% interest per year would yield $1,010 at the end of the year. But that is simple interest, paid only on the principal. Money in savings accounts will earn compound interest, where the interest is calculated based on the principal and all accumulated interest.

Benjamin Franklin provided an example of the power of compounding—dubbed snowballing—where $4,500 left to each of two American cities outperformed the rate of inflation over 200 years.

So in the case of savings accounts, interest is compounded, either daily, monthly, or quarterly, and you earn interest on the interest earned up to that point. The more frequently interest is added to your balance, the faster your savings will grow. So with daily compounding, every day the amount that earns interest grows by another 1/365th of 1%. At the end of the year, the deposit has grown to $1,010.05.

Okay, $0.05 more doesn't sound like much. But at the end of 10 years, your $1,000 would grow to $1,105.17 with compound interest. Your 1% interest rate, compounded daily for 10 years, has added more than 10% to the value of your investment.

Yes, this still might not seem like much, but now consider what would happen if you were able to save $100 a month and add it to that original deposit of $1,000. After one year, you would have earned $16.05 in interest, for a balance of $2,216.05. After 10 years, still adding just $100 a month, you would have earned $725.50, for a total of $13,725.50.

Still not a fortune, but it's a reasonable rainy-day fund. And that is the main purpose of a savings account. When money managers talk about "liquid assets," they mean any possession that can be turned into cash on demand. It is, by definition, safe from fluctuations in the stock market and real estate values. In real-people terms, it's the emergency stash.

The Snowball Effect

To truly understand the snowballing effect of compound interest, consider this classic test case, conducted by none other than Benjamin Franklin. The scientist, inventor, publisher, and Founding Father was a bit of a showman, so it must have given him a chuckle to launch an experiment that would not bear results until 200 years after his death in 1790.

In his will, Franklin left roughly the equivalent of $4,500 each to the cities of Boston and Philadelphia. He stipulated that it was to be invested at 5% annual interest for 100 years. Then, three-quarters of it was to be spent on a worthy cause while the remainder was to be reinvested for another 100 years.

In 1990, Boston's fund had about $5.5 million. Philadelphia's had about $2.5 million. Due to the effects of compound interest, both cities managed to outperform the rate of inflation over the 200 years. However, neither city came close to the combined $21 million that Franklin calculated they would achieve. The reason is that interest rates fluctuate over time, rarely achieving the 5% annual rate that Franklin assumed.

Start Early, Save Often

Still, Franklin's experiment demonstrated that compound interest can build wealth over time, even when interest rates are at rock bottom. It's quick and easy to find the current rates banks are offering by going online. Some banks specialize in high-yield savings accounts. The best savings accounts include those offered by banks where interest on the account is compounded daily and no monthly fees are charged. Banks often state their interest rates as annual percentage yield (APY), which reflects the effects of compounding. Note that the APY and annual percentage rate (APR) are not the same things, for APR doesn't include compounding. 

The Bottom Line

Unlike Benjamin Franklin, most of us have no desire to test what our savings might be worth in 200 years. But we all need to have a little money set aside for an emergency. Compound interest, combined with regular contributions, can add up to a decent emergency nest egg.