# Knowing How Savings Account Interest Is Calculated

Banks Editorial Team · November 21, 2018

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 which 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.

## Banking and How 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 isn’t always straightforward so you’ll want to know exactly how savings account interest is calculated. We’ll cover that, along with how banks set those interest rates, below.

Savings accounts may offer an APY or compound interest rates, so we’ll look at how savings account interest is calculated in both cases. 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).

## How to Calculate Savings Interest Rates

However, some banks will not quote the APY but rather a compound interest rate, for which the frequency of interest payments will need to be taken into consideration as the interest earned will be compounded, or added to the deposit. If a bank pays compound interest on a monthly or quarterly basis, those interest earnings to the principal on a monthly or quarterly basis. 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 is the initial amount deposited in the savings account (the Principal)
• r is the annual interest rate
• n is 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 is 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

So if 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.

## 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. You’ll find that it is related to the rate which the US central bank is charging on loans to member banks, or what’s called the Federal Reserve Discount Rate. If the US 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 and encourage saving, and stop inflation. So if a higher Federal Reserve Discount Rate is offered by the US central bank to banks borrowing money from them, rates on loans offered by banks to consumers can also be higher, and so 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 US 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 US central bank. The US 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 using this online comparison tool.

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