What Is Compound Interest? | Investopedia

Summary

This script explains the concept of compound interest, contrasting it with simple interest. With simple interest, an investment of $10,000 at 5% yields $500 annually for three years, totaling $1,500. Compound interest, however, calculates interest on the initial investment plus accumulated interest, resulting in $1,576.25 over the same period. The script emphasizes the power of compounding, especially over longer durations, as interest earnings grow exponentially.

Takeaways

• 📈 Compound interest is calculated on the initial principal and all accumulated interest.
• 🔢 To grasp compound interest, it's helpful to compare it with simple interest first.
• 💼 Simple interest is calculated only on the original principal amount.
• 💵 If you deposit $10,000 at a 5% simple interest rate for three years, you earn $500 per year, totaling $1,500 in interest.
• 📊 With compound interest, the interest for the second year is calculated on the original principal plus the interest from the first year.
• 🌐 In the third year, compound interest is calculated on the total amount including interest from the first two years.
• 💹 Over three years, $10,000 at 5% compounded annually yields $1,576.25 in interest, compared to $1,500 with simple interest.
• 🚀 The difference between compound and simple interest grows larger over time due to the compounding effect.
• 🌟 The power of compounding becomes more significant as time periods extend and the interest earned grows.
• ⏳ The longer the investment period, the more the compound interest will accumulate, highlighting the importance of starting to invest early.

Q & A

What is compound interest?

Compound interest is the interest earned on the original investment plus all the interest earned on the interest that has accumulated over time. It can be thought of as 'interest on interest'.

How does simple interest differ from compound interest?

Simple interest is calculated only on the original principal, whereas compound interest is calculated on the principal and the accumulated interest.

How much interest is earned on $10,000 with a 5% simple interest rate over 3 years?

The interest earned is $500 per year, for a total of $1,500 over 3 years.

What is the interest earned in the first year if $10,000 is invested at 5% interest compounded annually?

The interest earned in the first year is $500.

How is the interest calculated in the second year for compound interest?

In the second year, interest is calculated as 5% of $10,500 (the original $10,000 plus $500 from year one), resulting in $525.

What is the total amount of interest earned by the end of the third year with compound interest?

The total interest earned by the end of the third year is $1,576.25.

How much more interest is earned with compound interest compared to simple interest over 3 years?

With compound interest, $76.25 more is earned compared to simple interest over 3 years.

Why does compound interest result in a larger amount of earned interest compared to simple interest?

Compound interest results in a larger amount because it includes interest on previously earned interest, which increases the total interest earned over time.

How does compounding become more powerful over time?

Compounding becomes more powerful over longer periods because the interest earned grows larger as it accumulates on both the principal and the previously earned interest.

What would be an example of the principal in a compound interest scenario?

In the example provided, the principal is the original $10,000 investment.

Outlines

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💹 Understanding Compound Interest

This paragraph explains the concept of compound interest, contrasting it with simple interest. Compound interest is described as interest earned on both the original investment and the accumulated interest over time. The example given is a $10,000 deposit at a 5% interest rate. With simple interest, the investor earns $500 per year for three years, totaling $1,500. In contrast, with compound interest, the interest earned increases annually because it is calculated on the growing balance. After the first year, the investor earns $500. In the second year, the interest is calculated on the original $10,000 plus the $500 earned in the first year, resulting in $525. The third year's interest is calculated on the new balance of $10,500, yielding $550. Over the three years, the total interest earned with compound interest is $1,576.25, which is $76.25 more than with simple interest. The paragraph emphasizes that compound interest becomes significantly more powerful over longer periods as the interest earned compounds annually.

Keywords

💡Compound Interest

Compound interest is the interest earned on an initial investment as well as on the accumulated interest from previous periods. It is a fundamental concept in finance and investing, where the interest is calculated periodically and added to the principal, so that in the next period, the interest is earned on the increased amount. In the script, compound interest is illustrated by comparing it with simple interest. The example given is of a $10,000 investment at 5% interest compounded annually, where the interest earned each year is added to the principal for the calculation of the next year's interest.

💡Interest

Interest is the cost or return paid or received for the use of money. It is typically expressed as a percentage of the principal amount. In the context of the video, interest is the amount an investor earns on their investment. The script explains that with simple interest, the interest is calculated only on the principal, whereas with compound interest, it is calculated on both the principal and the accumulated interest.

💡Investment

An investment is an asset or item acquired with the goal of generating income or appreciation in value. In the script, the term is used to describe the act of depositing money into a savings account with the expectation of earning interest over time. The investment in question is $10,000, which is the principal amount used to calculate the interest in both simple and compound interest scenarios.

💡Principal

The principal is the original amount of money invested, lent, or borrowed. It serves as the base amount for interest calculations. In the script, the principal is the initial $10,000 deposited into the savings account. The concept is crucial in understanding how interest accumulates over time, as it is the amount on which interest is initially calculated.

💡Simple Interest

Simple interest is calculated only on the principal amount, without considering the accumulated interest from previous periods. It is a straightforward interest calculation method. The script contrasts simple interest with compound interest by stating that for a $10,000 investment at a 5% simple interest rate over three years, the total interest earned would be $1,500, calculated as 5% of $10,000 each year.

💡Annually

Annually refers to something that happens or is calculated once every year. In the context of the script, interest is compounded 'annually,' meaning the interest is added to the principal once a year, and the new total becomes the base for the next year's interest calculation. This is a key factor in how compound interest grows over time.

💡Accumulated Interest

Accumulated interest refers to the total interest that has been earned over a period of time, including interest that has been added to the principal. The script uses this concept to explain how compound interest works, as the interest from the first year is added to the principal, and then the interest for the second year is calculated on this new, higher amount.

💡Time Period

A time period is a duration of time, often used in finance to define the length over which an investment is held or an interest rate is applied. In the script, the time period is specifically three years, during which the interest on the initial investment is calculated and compounded annually.

💡Effective Compounding

Effective compounding refers to the process by which the power of compound interest becomes more pronounced over longer periods. It is the concept that as time passes, the amount of interest earned not only on the principal but also on the accumulated interest increases exponentially. The script mentions that 'effective compounding becomes especially powerful over longer time periods' to emphasize the benefits of long-term investment.

💡Interest Rate

The interest rate is the percentage at which interest is paid or earned on an investment. In the script, the interest rate is 5% for both the simple and compound interest examples. It is a critical factor in determining the amount of interest earned, as it dictates the proportion of the principal on which the interest is calculated.

💡High Interest Savings Account

A high interest savings account is a type of bank account that offers a higher interest rate than a regular savings account. It is a context in which the script's examples are set, where the investor deposits money to earn interest. The account is used to illustrate the difference between simple and compound interest over a three-year period.

Highlights

Compound interest is interest earned on both the original investment and accumulated interest over time.

Simple interest is calculated only on the original principal amount.

For a $10,000 deposit with a 5% simple interest rate over three years, the total interest earned is $1,500.

With compound interest, the interest earned each year is added to the principal for the next year's interest calculation.

In the first year of compounding at 5%, the interest earned is $500 on a $10,000 deposit.

In the second year of compounding, interest is calculated on the original amount plus the first year's interest, resulting in $525.

By the third year, compound interest on a $10,000 deposit at 5% results in an interest payment of $551.25.

Total interest earned with compounding over three years is $1,576.25, compared to $1,500 with simple interest.

The difference between compound and simple interest over three years is $76.25.

Compound interest becomes more powerful over longer periods as the earned interest accumulates.

The concept of 'interest on interest' is fundamental to understanding compound interest.

The example of a high-interest savings account illustrates the workings of simple and compound interest.

The importance of compound interest is highlighted by comparing it with simple interest over the same period.

The transcript explains the mathematical difference between simple and compound interest.

The transcript provides a clear example of how compound interest accumulates over time.

The transcript emphasizes the significance of compound interest in long-term investments.

The transcript suggests that compound interest can significantly outperform simple interest.

The transcript explains the impact of compound interest on the growth of investments.

The transcript provides a numerical comparison to demonstrate the power of compound interest.

Transcripts

compound interest is the interest and

investor earns on his original

investment plus all the interest earned

on the interest that has accumulated

over time it is easier to think of

compound interest as interest on

interest to understand compound interest

let's first look at simple interest the

interest earned on the original

principal only suppose you deposit ten

thousand dollars into a high interest

savings account and a five percent

simple interest rate for three years the

interest you earn each year is 5% times

ten thousand which equals five hundred

dollars for a total of fifteen hundred

dollars of interest at the end of year

three five hundred dollars plus 500 plus

five hundred now instead

suppose that you deposit the same ten

thousand dollars at 5% interest

compounded annually in year one the

interest you earn is the same five

hundred dollars but in year two the

interest you earn is 5% times ten

thousand five hundred the original

amount plus the interest you earned in

year one so the second year's interest

is five hundred twenty-five dollars in

year three you earn five percent

interest on eleven thousand twenty-five

dollars ten thousand dollars plus five

hundred year one interest plus five

hundred 25 year two interest or an

interest payment of five hundred fifty

$1.25 in total you earn one thousand

five hundred seventy six dollars and

twenty five cents in interest over three

years with compounding interest versus

fifteen hundred dollars with simple

interest a difference of seventy six

dollars and twenty five cents the

effective compounding becomes especially

powerful over longer time periods as the

amount of earned interest becomes larger

and larger