A:

## What is Compound Interest?

Compound interest, also known as compounded interest, is interest that's calculated both on the initial principal of a deposit or loan, and on all previously accumulated interest.

For example, let's say \$100 represents the principal of a loan, which carries a compounded interest rate of 10%. After one year you have \$100 in principal and \$10 in interest, for a total base of \$110. In year two, the interest rate (10%) is applied to the principal (\$100, resulting in \$10 of interest) and the accumulated interest (\$10, resulting in \$1 of interest), for a total of \$11 in interest gained that year. The second year's increase is \$11, instead of \$10, because the interest is compounding – that is, it's being applied to a larger base (\$110 compared to \$100, our starting point). Each year, the base increases by 10%: \$110 after the first year, then \$121 after the second year.

## What Is The Formula for Compound Interest?

It's similar to the Compounded Annual Growth Rate (CAGR). For CAGR, you are computing a rate which links the return over a number of periods. For compound interest, you most likely know the rate already; you are just calculating what the future value of the return might be.

For the formula for compound interest, just algebraically rearrange the formula for CAGR. You need the beginning value, interest rate, and number of periods in years. The interest rate and number of periods need to be expressed in annual terms, since the length is presumed to be in years. From there you can solve for the future value. The equation reads:

Beginning Value * (1 + (interest rate/number of compounding periods per year))^(years * number of compounding periods per year) = Future Value

This formula looks more complex than it really is, because of the requirement to express it in annual terms. Keep in mind, if it's an annual rate, then the number of compounding periods per year is one, which means you're dividing the interest rate by one and multiplying the years by one. If compounding occurs quarterly, you would divide the rate by four, and multiply the years by four.

## Calculating Compound Interest in Excel

Financial modeling best practices require calculations to be transparent and easily auditable. The trouble with piling all of the calculations into a single formula is that you can't easily see what numbers go where, or what numbers are user inputs or hard-coded.

There are two ways to set this up in Excel. The most easy to audit and understand is to have all the data in one table, then break out the calculations line by line. Conversely, you could calculate the whole equation in one cell to arrive at just the final value figure. We recommend the first approach, but both are detailed below.

In the example below, you can input the data in yellow, and choose the compounding period.

RELATED FAQS
1. ### Simple versus compound interest

Different methods in interest calculation can end up different interest payment. Learn the differences between simple and ... Read Answer >>
2. ### Continuous compounding versus discrete compounding

Learn to differentiate between and calculate the continuous and discrete compounding formulas and see how it is going to ... Read Answer >>
3. ### Mutual Funds and Compound Interest

Learn how mutual funds can grow wealth over time through the magic of compound interest by reinvesting dividends back into ... Read Answer >>
4. ### What is the difference between stated annual return and effective annual return?

Essentially, the effective annual return accounts for intra-year compounding, and the stated annual return does not. Read Answer >>
Related Articles
1. Investing

### Understanding the Power of Compound Interest

Understanding compound interest is important for both investing and borrowing money.
2. Investing

### Learn simple and compound interest

Interest is defined as the cost of borrowing money or the rate paid on a deposit to an investor. Interest can be classified as simple interest or compound interest.
3. Personal Finance

### How Interest Rates Work on Savings Accounts

Here's what you need to know to grow your rainy-day fund.
4. Investing

5. Investing

### The Effective Annual Interest Rate

The effective annual interest rate is a way of restating the annual interest rate so that it takes into account the effects of compounding.
6. Investing

### 4 Ways Simple Interest Is Used In Real Life

Simple interest works in your favor when you're a borrower, but against you when you're an investor.
7. Investing

### The Interest Rates: APR, APY And EAR

When most people shop for financial products, all they focus on is the listed interest rate. Human eyes instinctively dismiss the fine print, which usually includes the terms APR (annual percentage ...
8. Personal Finance

### Schedule Loan Repayments With Excel Formulas

Learn how to calculate all the particulars of a loan using Excel, and find out how to set up a schedule of repayment for a mortgage or any other loan.

### The Awesome Power of Compounding

The power of compounding. It may not be sexy, but it is the surest way to accumulate wealth over time.
RELATED TERMS
1. ### Compound Interest

Compound Interest is interest calculated on the initial principal ...
2. ### Continuous Compounding

Continuous compounding is the process of calculating interest ...
3. ### Compounding

Compounding is the process in which an asset's earnings, from ...
4. ### Discrete Compounding

Discrete compounding refers to the method by which interest is ...
5. ### Future Value - FV

Future value (FV) is the value of a current asset at a date to ...
6. ### Compound

Compound is the ability of an asset to generate earnings, which ...
Hot Definitions

An investment advisor is any person or group that makes investment recommendations or conducts securities analysis in return ...
2. ### Gross Margin

A company's total sales revenue minus its cost of goods sold, divided by the total sales revenue, expressed as a percentage. ...
3. ### Inflation

Inflation is the rate at which prices for goods and services is rising and the worth of currency is dropping.
4. ### Discount Rate

Discount rate is the interest rate charged to commercial banks and other depository institutions for loans received from ...
5. ### Economies of Scale

Economies of scale refer to reduced costs per unit that arise from increased total output of a product. For example, a larger ...
6. ### Quick Ratio

The quick ratio measures a company’s ability to meet its short-term obligations with its most liquid assets.