When researching bank options, it is important to understand how savings account interest is calculated. Banks may quote the rates paid on their savings account as the APY (annual percentage yield), which is used to determine interest earned using simple interest rate calculation, or with a compound interest rate which requires a more complex calculation that factors in the frequency of interest payment (daily, monthly, quarterly or annually). We explain how savings account interest is calculated in either scenario and how banks set the interest rate offered on their savings accounts. There are plenty of online monthly savings calculators that do the math for you. But learning to make sense of the numbers can help you understand the specifics of why you are receiving as much (or as little) as you are.

## What is Interest on a Savings Account?

At its simplest, interest is the cost of borrowing money. Generally, you’ll pay interest to borrow money, and you can collect interest when you lend money. When you put money in a savings account, the bank is technically borrowing the money and paying you interest in return.

## How a Savings Account Interest is Calculated

When you’re looking to open a savings account with your bank, probably the most important factor is the money you’ll be earning on that deposit. That will relate directly to the interest rate on the savings account, but the calculation of interest rate on savings depends on whether your bank uses simple or compound interest formulas.

### Simple Interest

Simple interest, as the name suggests, is the most straightforward to calculate. The information from the bank that you will need is just the rate known as the APY (annual percentage yield), which is then multiplied by the amount deposited (known as the principal) and the number of years that the deposit is held in the savings account. So for example, if you deposit $5,000 in a savings account with an APY of 1%, in one year you will earn $50 interest ($5,000 x 0.01 x 1). If you leave the deposit for another year, another $50 interest will be earned so that over the 2 years, total interest earned will be $100 ($5,000 x 0.01 x 2). For 3 years, total interest is $150, 4 is $200 and so on. The main point to remember is that no matter how much you have in your savings account, interest will only be earned on your initial deposit.

### Compound Interest

However, some banks will not quote the APY but rather a compound interest rate. In this case, the frequency of interest payments will need to be taken into consideration as the interest earned will be compounded, or added to the deposit. Compound interest calculates your interest using your principal balance plus any interest you’ve already earned over a certain amount of time. If a bank pays compound interest on a monthly or quarterly basis, those interest earnings to the principal will occur on a monthly or quarterly basis. The more often your bank compounds, the more your balance will grow. Compound interest can build wealth over time, even when interest rates are at their lowest.

A simple example of how compounding works is to imagine if someone gives you a penny every day and promises to double the amount each day. At the end of the month you would have millions of pennies. Of course that’s a compound interest rate of 100% which is unheard of, but it’s a simple illustration of how compounding is advantageous and why you should try to find a bank that offers it.

In this more complex case, we will assign the variables with letters so that we can see the compound interest rate calculation as a formula to show how savings account interest is calculated in this scenario.

- P = the initial amount deposited in the savings account (the Principal)
- R = the annual interest rate
- n = the number of times that interest is calculated in the year (i.e. if the interest is paid on a monthly basis, n will be 12, or if it is paid on a quarterly basis, n will be 4)
- t = the number of years that the deposit is held in the savings account

The annual interest amount earned is then [P x (1 + r/n)^nt] – P

If you’re having a bad Algebra class flashback, don’t worry! We’ll break it down for you. Let’s say you’re thinking of depositing your $5,000 in a savings account offering 1% compound interest rate, paid on a monthly basis, at the end of one year you will have earned $50.23 [($5,000 (1+(0.01/12))^12]-$5,000

If you were to leave your money in for 2 years, the interest earned at the end of the 2 years would be $100.96 [($5,000 (1+(0.01/12))^(12×2)]-$5,000. This is because interest is being earned on the initial $5,000 plus the $50.23 interest you earned in that first year.

## How Do Banks Set Interest Rates

Now that you understand how savings account interest is calculated, it’s worth also understanding how the banks set those interest rates on savings accounts. It is related to the rate which the U.S. central bank is charging on loans to member banks, or what’s called the Federal Reserve Discount Rate. If the U.S. central bank increases its interest rate, commercial banks will follow; whether they borrow directly from the US central bank, or from other banks, all interest rates will tend to rise as the cost of borrowing will increase and so this cost will be passed on. This is part of a contractionary monetary policy, designed to discourage lending, encourage saving, and stop inflation. So, if a higher Federal Reserve Discount Rate is offered by the U.S. central bank to banks borrowing money from them, rates on loans offered by banks to consumers can also be higher, and rates on savings accounts can also be increased for the bank to still be in a profitable position.

Conversely, if the government is seeking to stimulate economic growth and increase lending using expansionary monetary policy, the U.S. central bank will lower the Federal Reserve Discount Rate. In turn, the interest rates offered by banks on both loans will decrease. And because the banks will seek to generate more income on the interest paid by customers on loans than the interest paid out to customers on savings accounts, the interest rates on savings accounts will need to lower. Although banks don’t all follow a set formula, in order to remain competitive with other banks they will need to follow the same trends, led by the U.S. central bank. The U.S. central bank rate will, therefore, help determine the interest rate set on a savings account, and the methods outlined above regarding simple and compound interest explain how savings account interest is calculated. You can compare savings account interest rates offered by a range of banks clicking here.

## Key Takeaways

- Compound interest is interest calculated on principal and earned interest from previous periods; simple interest is only calculated based on principal
- Compounding period matters – the more often you earn interest, the faster your money could grow
- The longer you keep your money in the account, the more opportunities it has to grow

Also remember, the interest rate on savings accounts fluctuates and that impacts how much you’re earning. Consider online banks which don’t have the same overhead as brick-and-mortar banks. They can often offer better services and higher returns to their customers. While it may seem like a small amount, every little bit helps and adds up over time. Depending on the interest rate and how it’s calculated, you could end up with quite a nice sum if you’re patient.