What Is Interest Earned on Savings?

How to Calculate Interest Earned on Savings

Interest on savings fourmual

 © The Balance, 2018

Interest earned on savings is the money earned when you place it in a savings account. It's important to know how to calculate it, so you can compare the savings accounts from different banks and find the one that will work for you while it helps your money grow.

Definition and Examples of Interest Earned on Savings

Interest is the cost of borrowing money. When someone lends you money, you're normally charged a percentage of the amount you borrowed as payment to the lender. Interest is an agreed-upon amount but can change based on various circumstances and whom you borrow from.

You might not realize that banks borrow money from you when you place it in your savings account. That is why you receive interest; it is also an incentive for you to keep your money in a savings account.

There is no insidious intent behind a bank using your money in this way; it is used to create loans for other customers and keep money flowing through the economy. The bank also makes money, because it charges other people more interest than it pays you.

How to Calculate Interest Earned on Savings

To calculate the interest earned from your savings account, gather the following pieces of information:

  • Principal: This is your account balance at the amount you lend to the bank. The variable “p” stands for "principal," or the amount in your account.
  • Interest payment frequency: This is how often the bank pays you interest (yearly, monthly, or daily, for example). The variable “n” represents the number of times per year interest is paid.
  • Interest rate: This is the percentage that the account pays you. The variable “r” is converted to a decimal.
  • Term: This is the overall length of the loan in years, represented by "t." You'll need to convert months to years for this variable. For example, one month is .083 years, two months are .167 years, and 18 months are 1.5 years.

Once you have the information, you can plug it into the simple or compound interest formulas to figure out the interest earned on your savings. For example, the interest you earn in one period is simple interest and can be calculated with this formula:

simple interest 2

The interest you earn in a savings account is compounding interest, which means that what you earn is added to the balance, and then that amount collects interest, and the pattern continues. To calculate compounding interest, use this formula:

Compound interest formula

Where the variables are:

  • A= the total value in the future
  • P= the initial deposit
  • r= the interest rate
  • n= the number of compounding periods
  • t=the number of periods that have passed or will pass

Tip

For a quick answer or to check your calculations, you can use a compound interest calculator. Your results may differ when you use the online calculator.

How Interest Earned on Savings Works

Once you have the information you need, you can figure out the interest you can expect to earn.

Calculating Simple Interest

The formula for calculating simple interest, or the interest gained over one period, is relatively easy:

If you put $100 in your savings account that earns 5% per year, you'd calculate how much interest you'd earn as such:

  1. A = $100 x .05 x 1
  2. A = $100 x.05
  3. A = $5

Since saving accounts compound interest, this calculation only gives you the first period's interest earned. The compound interest formula gives you the total amount you'll have after a certain number of periods, instead of only telling you how much interest you've earned.

Calculating Compound Interest

To calculate compound interest on a savings account, your formula needs to take two things into account:

  • More frequent periodic interest payments: Many interest-bearing accounts pay interest more than once per year. For example, your bank might pay interest monthly.
  • An increasing account balance: Any interest payments will alter subsequent interest calculations.

Here, you add the assumption that your bank pays interest monthly. Use this compound interest formula to calculate the ending amount after one year (A):

If you were to deposit $100 in your savings account that earns a 5% annual percentage yield, compounding monthly for one year, you'd calculate it like this:

  1. A = $100 [ 1 + (.05 ÷ 12) ] 12 * 1
  2. A = $100 [ 1 + ( .004167 ) ] 12
  3. A = $100 [ 1.004167 ] 12
  4. A = $100 [ 1.0512 ]
  5. A = $105.12

In this example, your account earned $5.12.

Calculating Annual Percentage Yield

As the equation demonstrates, monthly compounding increases your annual returns. While the simple interest equation earned $.42 per month, the monthly compounding equation averaged $.43 ($5.12 ÷ 12). This difference is important to understand, as your interest rate is generally quoted as the annual percentage yield (APY). You'll also use it when you’re calculating interest for one year or more. Most banks advertise APY for interest-bearing accounts—the number is usually higher than the "interest rate," and it's easy to work with because it accounts for compounding.

Even though the interest rate in both examples is 5%, the APY in the compounding example is 5.12%, calculated like this:

APY
  1. APY = ( 1 + (.05 ÷ 12 ) ) 12 - 1
  2. APY= ( 1 + .004167 ) 12 - 1
  3. APY = ( 1.004167 ) 12 - 1
  4. APY = 1.0512 - 1
  5. APY = .0512 or 5.12%

The APY is higher than the stated annual rate when banks pay interest more often than annually. The APY tells you exactly how much you’ll earn over a year, without the need for complicated calculations.

The additional .12% earned might not seem like much, but the earnings grow as you save more money and leave it in an interest-bearing account longer.

Accounting for Ongoing Savings With Deposits

The examples above assume you make a single deposit, but that's rarely how people save. It's more common to make small, regular deposits into a savings account. With a little adjustment to the formula, you can account for those additional deposits.

If you make regular deposits to your account at the end of each month instead of a single lump-sum deposit, you need to modify your calculation or your spreadsheet formula.

Everything in the following examples will remain the same as the monthly compounding equation above, but instead of an initial deposit of $100, assume you start at $0 and plan to make monthly deposits of $100 over the next five years.

To calculate by hand, use the future value of an annuity formula. In this equation, "FV" is the future value of your account with deposits and compounding interest, "Pmt" is the monthly payment amount, "r" is the monthly interest rate, and "n" is the number of months.

Here's the formula for a series of identical periodic deposits over a five-year period:

Future value of an annuity
  1. FV = $100 x [ { ( ( 1 + 0.004167 ) 60 ) – 1 } ÷ 0.004167 ]
  2. FV = $100 x [ { 1.283 – 1 } ÷ 0.004167 ]
  3. FV = $100 x 68.0067
  4. FV = $6800.68

How to Calculate Interest Earned on Savings With a Spreadsheet

Spreadsheets can automate the process for you and allow you to make quick changes to your inputs.

To calculate your interest earnings with a spreadsheet, you'll need to use the future value calculation. The future value is the amount your asset will be worth at some point in the future, based on an assumed growth rate. Microsoft Excel and Google Sheets (among others) use the code “FV” for this formula.

To make a spreadsheet from scratch, start by entering the following in any cell to figure your simple interest earnings:

Future value spreadsheet formula

That formula asks for the following items, separated by commas:

  • Interest rate (5% in the example)
  • Number of periods (interest is paid once per year)
  • Periodic payment (this simple example assumes you won't make future deposits)
  • Present value ($100 initial deposit)

The formula above shows simple interest (not compound interest), because there is only one compounding period (annual). Because of spreadsheet programming and accounting concepts, you'll need to enter your payment as a negative number to get a positive number on the sheet.

For a more advanced spreadsheet, enter the rate, time, and principal in separate cells. Then you can refer to those cells from your formula and easily change them for different situations.

Extra Steps for Compounding Scenarios

To use this spreadsheet formula for an account with compounding interest, you need to adjust several numbers. To change this annual rate to a monthly rate, divide 5% by 12 months (0.05 ÷ 12) to get 0.004167. Next, increase the number of periods to 12. To calculate monthly compounding over multiple years, you’d use 12 periods per year. For example, five years would be 60 periods.

In this case, your spreadsheet formula would look like this:

Sample 5 year FV

You'd end up with $6,800.68 after five years.

Key Takeaways

  • Interest on savings accrues when you deposit money into an interest-bearing savings account.
  • There are two main types of interest: compound and simple interest.
  • If you aren't interested in doing the math yourself, online calculators and spreadsheet templates can help simplify the process.