# Formulas and Examples to Calculate Interest on Savings

## Free Spreadsheet Templates, and Instructions to DIY

As you grow your savings, it’s helpful to learn how to calculate interest. Doing so allows you to plan for the future and better understand your progress toward your goals. It’s easy to calculate the interest you earn, especially when you use free spreadsheets or online calculators.

Here, you'll learn how to calculate the following:

- Simple interest
- Single investments (one-time deposits)
- Compound interest
- Ongoing investments (monthly deposits, for example)

Just want an answer? Use this calculator example in Google Sheets to calculate interest (you will need to copy the spreadsheet into another document for your own use).

## How to Calculate Interest You Earn

Interest is the cost of borrowing money. When you lend money you typically get your money back plus a little bit extra. That extra amount is the "interest," or your compensation for letting somebody else use your money. The same is true when you deposit funds into an interest-bearing account.

When you make deposits into savings accounts or certificates of deposit (CDs) at a bank or credit union, you’re lending your money to the bank. The bank takes the funds and invests, possibly lending that money to other customers.

### Get Organized

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

**The amount of your deposit**, or the amount you lend, using the variable “p” for "principal."**How frequently to calculate**and pay interest (yearly, monthly, or daily, for example), using “n” for the number of times per year.**The interest rate**, using “r” for the rate in decimal format.**How long you earn interest for**, using “t” for the term (or time) in years.

### Simple Interest Example

Assume you deposit $100 at your bank, you earn interest annually, and the account pays 5%. How much will you have after one year?

For the most basic calculation, start with the simple interest formula to solve for the interest amount (i).

### Simple interest formula:

- p x r x t = i
- $100 deposit x 5% interest x 1 year term = $5
- $100 x 0.05 x 1 = $5

The calculation above works when your interest rate is quoted as an annual percentage yield (APY), and when you’re calculating interest for a single year. Most banks advertise APY—the number is usually higher than the "interest rate," and it's easy to work with because it accounts for compounding.

## Calculating Compound Interest

Compounding occurs when you earn interest on a deposit or loan, and then the money you earned generates additional interest.

With compound interest, you earn interest on the interest earnings you previously received.

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.

### Compound Interest Example

For the compound interest example, stick with the same information as the simple interest example, but add the assumption that the bank pays interest monthly. Use this formula for compound interest to calculate the ending amount after a year (A):

### Compound interest formula:

- A = P (1 + r ÷ n) ^ nt
- A = $100 x (1 + 0.05 ÷ 12) ^ (12 x 1)
- A = $100 x (1.004167) ^ (12)
- A = $100 x 1.051
- A = $105.1166 (or $105.12 if your bank rounds up)

If it’s been a while since your last math class, the caret symbol (^) represents an exponential equation, which means a number is raised to the power of another. For the example here, “1.004167 ^ 12” means "1.004167 raised to the power of 12. You can avoid the caret symbol by using superscript formatting: **A = P (1 + r/n) ^{nt}**.

### Compounding Increases APY

As the equation demonstrates, compounding monthly increases your annual returns. While the simple interest equation earned $5, the monthly compounding equation earned $5.12. Even though the interest rate in both examples is 5%, the APY in the compounding example is 5.12%. Whenever banks pay interest more frequently than annually, the APY is higher than the stated annual interest rate. The APY tells you exactly how much you’ll earn over a year, without the need for complicated calculations.

An extra 12 cents might not seem like much, but the earnings get more impressive as you save more money and leave it in an interest-bearing account for longer.

## Calculating 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, use a **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.

The spreadsheet link at the top of this article is already filled out for you with the 5% example. You can download that template and change the numbers for your own needs.

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

### Future value example:

**=FV(0.05,1,0,100)**

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 expression above uses the simple interest example from earlier. It shows simple interest (not compound interest) because there is only one compounding period (annual).

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, four years would be 48 periods.

## Accounting for Ongoing Savings

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.

### Monthly Deposits Example

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.

### Interest on a series of deposits:

=FV(0.004167,60,100)

Note that you use a monthly interest rate (5% ÷ 12 months), and you adjust the number of periods to 60 months.

To calculate by hand, use the **future value of an annuity** calculation. In this equation, "Pmt" is the monthly payment amounts, "r" is the monthly interest rate, and "n" is the number of months. Answers may vary due to rounding.

### Example of a series of deposits:

- FV = Pmt x (((1 + r) ^ n) – 1) ÷ r)
- FV = 100 x (((1 + 0.004167) ^ 60) – 1) ÷ 0.004167)
- FV = 100 x (1.283 – 1) ÷ 0.004167
- FV = 100 x 68.0067
- FV = 6800.67