# Compound Interest Definition, Example and Formula

At its core, compound interest is very simple. It is interest earned on top of interest. The longer your money compounds, the faster it grows.

The working principle behind compound interest is really quite simple. It’s just interest earned on top of interest. So, if you have £100 in a savings account that pays compound interest at a rate of 20% per year, then you would earn £20 in interest at the end of the year. The next year, your interest would be £24 based on your new balance of £120.

When applied to loans, compound interest can have a dramatic effect. Consider this example: You take out a £100,000 loan with an interest rate of 20% that is compounded yearly. Over the course of 30 years, you would end up paying back a total of £204,520.70, plus the original £100,000 that you took out.

Compound interest is a universal principle and works the same in the UK, US, Australia and around the world, regardless of which currency it’s expressed in.

There are a few terms that are related to compound interest that you should be familiar with before we start. These include:

- Accumulated value: The total value of an investment at any given point in time, which includes both the principal and the accumulated interest.
- Annual percentage yield (APY): A measure of how much interest is earned on an investment, or the rate of return, per year.
- Effective annual rate (EAR): The actual rate of interest that you would earn on an investment if it compounded yearly. This is often higher than the nominal annual rate because it takes into account compounding.
- Principal money – This is the value of money that’s invested or borrowed.
- Interest – The fee charged for borrowing money, typically expressed as a percentage of the principal amount per year.

There are some others that we’ll learn along the way, but for now, this should give a firm understanding of what’s coming.

## What is Compound Interest?

Compound interest is the interest that accrues on an initial principal sum and also on the accumulated interest of previous periods. It is basically “interest on interest,” and it helps your money grow at a faster rate than simple interest, which is calculated only on the principal sum.

To calculate compound interest, you need to know the principal sum, the annual interest rate, and the number of compounding periods per year.

Working out compound interest all starts with the principal money. This is a term used to describe the original sum of cash that is deposited or lent. The principal will always be the starting amount no matter how much interest has been added on top of it in previous periods.

Then, there’s the annual nominal interest rate (or APR). This number shows how much your investment will grow each year if left untouched. Nominal interest rates are variable and can go up or down.

The number of compounding periods per year is how often interest will be added to the account. In other words, it’s the frequency with which your principal will earn more money. The most common compounding periods are monthly or yearly, but some accounts may compound interest daily, weekly, or even continuously.

The payment frequency of compound interest can significantly impact how quickly your money grows. The more compounding periods there are in a year, the faster your principal will grow. However, it can really depend on the loan or credit you take out, so it’s important to make sure you’re clear on this before entering the contract.

The main benefit of using compound interest is that it can help your money grow faster than simple interest. This is great for savings accounts or investment ventures.

However, the main downside of compound interest is that it can work against you if you have a loan or credit with compounding interest. This is because the interest will be added not just on the original sum borrowed but also on all the accumulated interest. This will lead to higher charges overall.

### How Does Compound Interest Work?

To put this into real terms, let’s say you put £100 into a savings account that has offered a compound interest rate. If the annual rate is set at 12% (which is exceptionally high, but easy for this example), then your account will grow to £112 after one year (assuming you make no withdrawals over this time.

However, if the annual rate increases to 15%, your account will grow to £128.8 after the following year. This is because the interest from the first year (£12) will be added to the principal sum for the next year, and then that interest will also earn interest.

#### How Does Compound Interest Grow?

Compound interest is often described as ‘interest on interest’, and this phrase is an excellent way to think about how it works. The main reason compound interest can grow so quickly is that each time the interest is added to the account, it becomes part of the principal sum. This means that the next time interest is calculated, it will be based on a larger number, which can lead to exponential growth.

It’s important to remember that compounding periods have a big impact on how quickly your money will grow. The more compounding periods there are, the faster your money will grow.

An example of compound interest at work would be looking at an investment account. Say you deposit £3,000 into an investment account that had a 2% yearly compound interest rate, your savings would look a little something like this;

On the other hand, if you took out a £2,000 credit card with a compound interest rate of 15% (which is still below the average interest rate on a credit card), and you were looking to pay it off in five years, you would need to pay a minimum of £47.58 per month, but you would be paying over £854.80 in interest, which is nearly half the total loan amount.

## What are the Key Facts About Compound Interest?

If you want to remember Compound Interest most easily, then it’s worth taking the time to learn the key points of what makes this interest rate what it is.

- Compound interest is the addition of accrued interest to the principal sum, which then earns interest on its own.
- The frequency of compounding has a big impact on how quickly your money will grow. The more compounding periods there are, the faster your money will grow.
- Compound interest can work for you or against you, depending on whether you’re saving or borrowing money.

## What is the Formula for Compound Interest?

The compound interest formula is very simple: A = P(1 + r/n)nt, but don’t let this confuse you. We’ll break it down.

First, you must take your interest rate and convert it into a decimal. For example, a 5% interest rate would 0.05. in this case, we’ll also state that the principal sum borrowed is £10,000. The rest of the figures look like this;

A = Total amount included loaned amount plus interest

P = Principal amount (£10,000)

r = Annual nominal interest rate as a decimal (0.05)

R = Annual nominal interest rate as a percentage (5%)

n = number of compounding periods of time, i.e. 12 months in a year (12/yr)

t = the time period as a decimal (6 months is 0.5)

I = the total amount of interest

So, to solve A = P(1 + r/n)not where the loan is £10,000 with a 4% interest rate over five years (with monthly compounding interest), your calculation would look like this;

A = P(1 + r/n)nt

A = 10,000.00(1 + 0.04/12)(12)(5)

A = 10,000.00(1 + 0.003333333)(60)

A = £12,209.97

On a £10,000, five-year loan, you’ll be paying back the original £10,000, plus £2,209.97 in compounded interest.

The purpose of compounding interest is to make your money grow faster. The more frequently interest is compounded, the faster it grows. This is because every time interest is to be added to your savings account, you’re always getting interest on the amount in your account.

So, if you start with £100, and you gain 1%, you’ll have £101. Next time, you’ll get 1% interest on the £101 instead of the original amount. At these rates, this doesn’t make a huge difference immediately, but it certainly can over time.

However, when it comes to loans or credit, having an account with compounding interest means that you can end up paying a lot more money back to your loan provider over the loan term.

#### What are the Compound Interest Schedules?

There are three compound interest schedules, depending on the provider and the contract.

- A Continuous Compound Interest Schedule compounds interest daily.
- A monthly Compound Interest Schedule compounds interest monthly.
- An Annual Compound Interest Schedule compounds interest annually.

The type of schedule used can greatly impact your investment or savings overall growth. For example, if you have a credit card with a 20% APR, and you make a purchase of $100, the daily compound interest schedule would charge you $20 in interest per year total.

However, if you’re dealing with a monthly compound interest schedule, you’d be charged a total interest rate of £131.91, which makes such a big difference with your repayments and budget.

Interestingly, this is all worked out and managed by a concept known as accrual accounting.

#### What is a Compounding Period?

The compounding period is when accrued interest is added to the principal sum, and it can be monthly, yearly, or even daily. This will vary depending on several factors, including the loan provider, the contract, and the personal agreement of the loan itself.

The frequency of compounding has a big impact on how quickly your money will grow. In some cases, The compounding periods have a big impact on how quickly your money will grow, how long it will take for you to pay off your loan, or how much you’ll need to pay back in total.

When it comes to actually define how what the compounding period will be, it’s important to look at the loan agreement and/or credit card statement. This will spell out, in detail, how often interest is applied to the outstanding balance on your account.

Typically, these periods can range from daily to yearly, and it’s important to know which one your loan uses so you can accurately calculate the interest you’ll be charged. They are decided on by your credit provider.

#### How does the compound interest schedule affect the compound interest calculation?

Shorter compounding periods will lead to more interest being paid. This is a positive thing for savers, but a negative for borrowers. When taking out a loan that uses compound interest, for example, a bridging loan, a longer compounding period will lead to you paying less interest than one with a shorter compounding period. Of course, this is only true if all other terms remain the same.

#### How to Calculate Compound Interest

Compound interest is calculated by taking the original investment amount and multiplying it by one plus the annual interest rate raised to the number of compound periods minus one. The total number of compound periods is equal to the number of years multiplied by the number of compounding periods per year.

The best way to calculate it is using the formula which looks like this;

A = P(1 + r/n)nt

Legend

A = Total amount included loaned amount plus interest

P = Principal amount (£10,000)

r = Annual nominal interest rate as a decimal (0.05)

R = Annual nominal interest rate as a percentage (5%)

n = number of compounding periods of time, i.e. 12 months in a year (12/yr)

t = the time period as a decimal (6 months is 0.5)

I = the total amount of interest

However, the easiest way to do this would be to use a compound interest calculator, one of which can be found online on websites like this, that will handle the complicated maths on your behalf.

But, as an example, for now, say you take out a loan for £8,000 with an APR of 5%, compounding yearly with monthly payments over a five year period, the formula would look like this;

A = P(1 + r/n)nt

A = 5,000.00(1 + 0.05/12)(12)(5)

A = 5,000.00(1 + 0.004166667)(60)

A = £6,416.79

Yes, this is an insane amount of money, but that’s what happens if you compound monthly. On the other hand, if you compound yearly, the total interest paid, using the same formula, would be £6,381.41.

### Who Benefits from Compound Interest Most?

There are two types of people who benefit from compound interest the most.

The first type is people who start saving early on in their lives, as they will have more time for their money to grow. This is due to the fact that compound interest grows at a faster rate than simple interest, meaning that the earlier you start saving, the more time your money has to grow.

The second type of person who benefits from compound interest the most is people who can invest a large sum of money all at once. This is because the more money you have invested, the more interest you will earn, and the faster your money will grow.

However, financial lenders also benefit greatly from compound interest. This is because the Rule of 72 can be used to estimate how long it will take to pay off a loan, as well as how much interest you’ll end up paying. The more interest you pay, the more money your credit provider or lender will make.

As a borrower, you need to make sure you’re aware of how much you’ll pay and how much you could be at risk of paying.

## What types of loans use compound interest?

Bridging loans, overdrafts and credit cards are all examples of loan types that use compound interest. When searching for personal loans that uses compound interest, it’s always best to look for an amortisation schedule. This table shows how much of each payment goes towards the interest and how much goes towards the principal.

Here’s a more definitive list of loan accounts with compound interest;

- Bridging loans
- Overdrafts
- Credit cards
- Student loans
- Property development finance
- Business revolving credit facilities
- Property investor hunting licences

### Which Financial Products use compound interest most often?

The most common financial products operating with compound interest include;

- Savings accounts
- Stock market investments
- Fixed-term deposits

Of course, there are lots of other types of accounts with compound interest.

## How to get Compound Interest?

The simplest way is to invest in accounts with compound interest such as the following:

- A high interest savings account
- Stocks and shares
- Some peer to peer lending products

Securing high returns that compound over time can quickly add up.

## What is the History of Compound Interest?

The history of compound interest can be dated back to the 1700s when mathematician, Edmond Halley, discovered that money could grow exponentially over time. At the time, he was working on a problem related to insurance and realised that if you left your money invested instead of withdrawing it, you would earn more money in the long run.

Since then, compound interest has been used by individuals and businesses to grow their money. In the early 1900s, the bank’s interest definition of the time meant allowed them to begin offering savings accounts that paid compound interest. And in the mid-1900s, credit cards became widely available and began charging compound interest on balances.

Compound interest grew in popularity because it was a way for people to earn money without having to put in any additional effort. All you had to do was leave your money invested and let the interest grow. What’s more, if you were a lender, you could make more money on your lending, thus becoming a more profitable business.

### Why is Compound Interest Known as Compound?

The name “compound” interest is derived from the fact that the interest on a loan or investment is compounded or added to the original principal amount. This means that you will be paying interest on both the principal and the accumulated interest.

The literal definition of compound is “to increase by addition.” In terms of compound interest, this means that your interest will be added to your principal, and then the interest will be calculated on the new total. This process continues throughout the life of the loan or investment, resulting in exponential growth.

The term was coined by Albert Einstein, who is often quoted as saying, “Compound interest is the eighth wonder of the world. He who understands it earns it … he who doesn’t … pays it.”

#### Is Compound Interest Safe for Financial Well-Being?

As part of a well-managed financial situation, compound interest is perfectly safe. That said, there is no one definitive answer to this question that fits everyone. In general, compound interest can be a great way to grow your money and achieve financial security. However, it’s important to note that there is always some element of risk involved with investing in stocks or mutual funds.

Furthermore, if you’re carrying a high-interest credit card balance, the compound interest you’re paying can be detrimental to your financial well-being. In this case, it’s important to work on paying off your debt as quickly as possible so that you’re not wasting money on interest payments.

## What are the other types of interest besides compound interest?

Here’s a list of the other types of interest you may come across in the financial world;

- Simple Interest: This is the most basic type of interest and is typically used for short-term loans. With simple interest, you will only be charged on the principal amount of the loan.
- Fixed Interest: As the name suggests, fixed interest refers to an interest rate that remains constant over time. This type of interest is often used in mortgages and other long-term loans.
- Variable Interest: Unlike fixed interest, variable interest rates can fluctuate over time. This type of interest is typically used for lines of credit and credit cards.
- Discounted Interest: Discounted interest is a type of interest that is offered at a lower rate than the standard rate. This is often used as an incentive to encourage people to take out loans or make investments.
- Prime Interest: Prime interest is the interest rate that banks charge their most creditworthy customers. This is the benchmark interest rate that other rates are based on.

### What is the difference between compound interest and simple interest?

The main difference between the comparison of simple interest vs compound interest. That is, compound interest includes the accumulated interest in calculating the new total, while simple interest does not. As a result, compound interest will grow faster than simple interest.

An example of this would be if you had a £1,000 principal with a simple interest rate of five percent. At the end of one year, you would have £1,050 in total.

With compound interest, however, the accumulated interest would be added to the principal, resulting in a total of £1,051.16.

This may not seem like a lot, but it certainly adds up over time and with larger amounts. It also depends on your interest rate, your deposits, and your compounding period, i.e. whether it’s monthly or yearly.

## What are the economic terms related to compound interest?

The following are some economic terms that are related to compound interest;

Capital: This refers to the amount of money that has been invested or loaned.

Interest Rate: This is the percentage of money that will be charged on the principal amount, and it can be either fixed or variable.

Principal: This is the original amount of money that was invested or loaned.

Compounding Period: This is the frequency with which the interest will be added to the principal, and it can be either monthly or yearly.

Accumulated Interest: This is the total amount of interest that has been earned over time.

Amortisation Schedule: This table or chart shows how the principal and accumulated interest are paid off over time. It can be used to help you plan for your financial future.

Time Value of Money: The time value of money is the concept that money today is worth more than money in the future. This is because money today can be invested and earn interest, while money in the future cannot. As a result, compound interest is a powerful tool that can help you achieve your financial goals if used wisely.

Rule of 72:This is a rule of thumb that can be used to estimate how long it will take for an investment to double in value. To use this rule, divide 72 by the interest rate. This will give you the approximate number of years it will take for your investment to double.

Compound Annual Growth Rate: The compound annual growth rate (CAGR) is the rate at which an investment grows over time. It is often used to measure the performance of an investment over a period of time, such as five years or ten years.

Mutual Funds: Mutual funds are investments that are made up of a collection of stocks, bonds, and other securities. They are typically managed by a professional investment company, and investors can purchase shares in the mutual fund. This is a popular way to invest for retirement or other long-term goals.

Tax-Sheltered Account: A tax-sheltered account is an investment account that allows you to defer or avoid taxes on the earnings. This can be a powerful tool to help you grow your wealth, as it allows your money to compound without being taxed each year.

Zero-Coupon Bond: A zero-coupon bond is a bond that does not pay interest payments but instead is sold at a discount to its face value. The bond will mature at its face value, and the difference between the purchase price and the maturity value is the return on investment. Zero-coupon bonds can be an excellent way to invest for long-term goals, such as retirement.

### What is the relationship between Compound Interest Mortgage and Compound Interest?

The relation between compound interest mortgage and compound interest is that with a compound interest mortgage, your monthly payments are applied to both the principal and the interest, which results in the interest being charged on a smaller principal each month.

This can save you money over time, as the amount of interest you pay will be less. With a regular mortgage, the interest is only applied to the principal balance each month, resulting in you paying more interest over time. Compound interest can be a powerful tool to help you save money on your mortgage, and it is something that you should consider when you are shopping for a mortgage.

You can calculate how much you will save over the life of the mortgage by using a compound interest mortgage and then compare this to the savings that you would realise by using a regular mortgage. This can help you make the best decision for your situation.