How Interest Works on Savings Accounts

How Benjamin Franklin proved compound interest's snowballing effect

Knowing how interest on savings accounts works can help investors earn as much as possible on the money they save. Interest on a savings account is the amount of money a bank or financial institution pays a depositor for holding their money with the bank. In a way, a bank borrows money from their depositors by using the deposited funds to lend money to other customers. In turn, the bank pays the depositor interest for their savings account balance while simultaneously charging their loan customers a higher interest rate than what was paid to their depositors.

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.

If you reinvest the interest you earned on your savings account and the initial amount deposited, you'll earn even more money in the long term. This process of earning interest on your savings plus earning interest on all of the accumulated interest from previous periods is called compounding. Investors can use the concept of compounding interest to build up their savings and create wealth.

Interest on savings accounts is expressed in percentage terms. For example, let's say you have $1,000 in the bank; the account might earn 1% interest. Unfortunately, most banks pay less than 1% interest on savings accounts due to historically low-interest rates.

Interest on Interest

In performing a straightforward interest calculation, $1,000 that earned 1% interest in one year would yield $1,010 (or .01 x 1,000) at the end of the year. However, that calculation is based on simple interest, paid only on the principal or the deposited funds. Some investors, such as retirees, might withdraw the earned interest or transfer it to another account. The interest payments act as a form of income. If the interest is withdrawn, the depositor's account will earn simple interest since no interest would be earned on any past interest.

However, with interest rates being so low, many depositors may opt to leave the interest earned in their savings account. As a result, the money in the savings account would earn compound interest, where the interest is calculated based on the principal and all of the accumulated interest.

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

The Power of Compounding Interest

In savings accounts, interest can be 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. Using our $1,000 example earlier and applying 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 versus $1,010 via simple interest.

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

Again, the amount earned still might not seem like much, but consider what would happen if you could save $100 a month and add it to the original $1,000 deposit. 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.

Total Compounded Savings in 10 Years
Year Future Value at 1% Total Contributions
Year 0 $1,000 $1,000
1 $2,216.05 $2,200
2 $3,444.33 $3,400
3 $4,684.95 $4,600
4 $5,938.03 $5,800
5 $7,203.72 $7,000
6 $8,482.12 $8,200
7 $9,773.37 $9,400
8 $11,077.59 $10,600
9 $12,394.93 $11,800
10 $13,725.50 $13,000
Obtained via interest calculator from

Although the amount is not a fortune, it's a reasonably-sized rainy-day fund, which is one of the main purposes 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 an emergency fund that can be used for unexpected expenses such as medical bills or car repairs.

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 were 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 $4.5 million while Philadelphia's fund had about $2.5 million due to the effects of compound interest. 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), reflecting the effects of compounding. Note that the APY and annual percentage rate (APR) are not the same, for APR doesn't include compounding. 

What's compound interest compared with simple interest?

Compound is interest on your interest, or reinvesting accumulated interest from previous periods. Simple interest is paid only on the principal or the deposited funds.

What's the long-term benefit of compounding?

Investors can use the concept of compounding interest to build up their savings and create wealth. If you reinvest the interest you earned on your savings account and the initial amount deposited, you'll earn even more money in the long term.

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.

Article Sources
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  1. U.S. Securities and Exchange Commission, "Compound Interest Calculator."

  2. HistoryNet. "Ben Franklin’s Gift that Keeps on Giving."

  3. The New York Times. "From Ben Franklin, a Gift That's Worth Two Fights."