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What is compound interest? How it Works and How to Calculate it

Compound interest is one of the most powerful forces in financial planning. By enabling you to maximise your returns, it can help you reach your goals more quickly. So, what is compound interest, and why does it have such a massive effect on investment portfolios?

What is Compound Interest: Summary Table

❓ What is compound interest?Earning interest on interest already earned
💡 Benefits of compound interest?Your wealth to grow faster than with simple interest
🔎 Types of compound interest investment accounts?Dividend stocks
•Fixed income securities
•Exchange-traded funds (ETFs)
•Real estate investment trusts (REITs)
•High-yield savings account
🏷️ Compound interest formula?A = [P(1+r/n)^nt] – P

What is interest?

Let’s start by defining the word interest.

Interest, generally, is a cost paid by either a borrower or a deposit-taking financial institution to a lender/depositor. It is calculated as a percentage of the initial value being lent/deposited (known as the principal amount).

In the case of simple interest, it is simply calculated as a percentage of the principal amount, ignoring any increase or decrease in the value of this amount over time.

For example, If you’re earning 2% interest annually on a principal amount of £1,000, you’ll get £20 every year (2% of £1,000) for as long as you commit to it.

What is compound interest?

Compound interest is often referred to as “interest on interest”. This essentially means that compound interest is calculated on the principal amount as well as the interest accumulated previously.

To refer back to the previous example, in this case, the £20 you get as your 2% interest on your £1,000 is then added to the underlying value that interest is calculated from in year two. This means you’ll get 2% of £1,020; £20.40.

Compound interest helps a sum grow faster compared to simple interest and can maximise your returns, especially with larger values and over a long time horizon.

Compound interest investments

Now that we know the answer to ‘what is compound interest’, we are going to look at investments that compound. Compound interest investments are financial instruments that compound over time, like money market securities. These assets generate income, which is then invested for a more significant return. 

Income growth generated from compound interest investments is not linear. Instead, the increasing value of an investment is due to its principal’s interest and accumulated interest. Compound interest investments can be short-term or long-term investments, and the growth of your investment will depend on how risk-averse you are. 

Here are eight compound interest investments and accounts that will help you earn more money.

  1. Dividend stocks
  2. Fixed income securities such as treasury bills, notes and bonds
  3. Exchange-traded funds (ETFs)
  4. Real estate investment trusts (REITs)
  5. Certificates of deposit (CDs)
  6. High-yield savings account
  7. Individual Savings accounts (such as stocks and shares ISAs)
  8. Money market funds 

How to calculate compound interest

The compound interest formula is a mathematical equation that helps you calculate how much money you will earn on a savings or investment account. There are different ways to calculate compound interest.

The easiest way is to use the interest formula of compound interest. The interest formula of compound interest calculates the total amount you will receive at the end of a time period and the total compound interest payments.

Compound interest formula 

Compound interest formula

Where: 

  • A = Future value of an investment
  • P = Principal amount / Initial deposit
  • r  = Annual Interest rate (decimal)
  • n = The number of times interest compounds per time
  • t = The time or number of years the money was invested.

For example:

Suppose Mark makes an initial deposit of £5,000 and earns an annual interest rate of 7%, compounded monthly. How much will Mark have in 30 years?

Calculation

Compound interest = 5,000 * (1+0.07/12)(12*30)  – 5,000

Compound interest= (5,000 * 8.116) – 500 = 35,582.48

The total amount of interest compounded after 15 years is £35,582.48.

The future value of your investment after 30 years is £40,582.48.

Daily compound interest calculator

Daily compounded interest is interest that is added to the principal every day. The daily compounding may be higher than interest compounded monthly, quarterly or yearly because interest is charged on the principal and previous interests earned daily.

Daily compound interest calculators have made life easy. You can use a daily compound interest calculator to find out how much you will earn per day and don’t want to do the calculations yourself. There are several daily compound interest calculators online. All you want to do is search for them.

However, if you want to calculate the daily compound interest manually, you can find the formula written below.

Daily Compound interest formula

Daily compound interest formula

Where: 

  • A = Daily compound rate
  • P = Principal amount
  • r  = Annual interest rate (decimal)
  • n = The number of times interest compounds per time
  • t = The time or number of years the money was invested.

For example:

If Sarah puts £500 in a general investment account that pays an annual interest rate is 7%. What will be her daily compound interest after the 2 years?

Calculation

Daily compound interest = 500 * (1 + 0.07/365)(365*2) – 500

Daily compound interest = (500 * 1.150) – 500 = 75.13

The daily compound interest after 2 years is £75.13.

The future value of your investment after 2 years is £575.13.

The frequency of compounding

The rate at which compound interest grows depends on how often compounding occurs. The higher the number of compounding periods, the faster compound interest will grow. The rate of compounding typically occurs more frequently than once a year, with popular compounding intervals being quarterly, monthly and daily.

Imagine you now have £10,000 in an ISA that pays 2% interest on your savings once a year. So, after 12 months, you’ll have £10,200.

If you had put it in a savings account that paid 1% semi-annually, you’d have £10,201 after 12 months.

The first interest payment would be 1% on £10,000, taking the amount in your savings account to £10,100. The second interest payment would be 1% of £10,100, so £101 – bringing the total return in the year to £201.

Pros and Cons of compounding

Compound interest has both advantages and disadvantages for consumers and financial institutions. 

The advantage is that compound interest is a powerful tool for building wealth because it has a snowball effect and has the ability to grow wealth over time. The benefit of compounding is that even small investments can yield significant returns over time and with compound interest. In addition, the power of compounding is beneficial to young investors who start investing early in life. 

Compounding becomes a problem when you take out a loan as interest keeps on building on the initial principal amount. This disadvantage is an advantage to financial institutions such as lenders and credit card companies who apply compounding interest to the repayment of loans. This interest can grow into something bigger than you ever imagined if you don’t pay attention to it or miss regular payments.

Impact of compound interest on pension

To highlight the impact this could have on your pension, imagine you’re offered two options you may choose from: £500,000 today or 1p today doubled every day for 30 days. Which would you choose?

Whilst you might jump at the chance of having £500,000 today, you could get over £5 million if you went for the second option – 1p, which is doubled every day for 30 days.

Of course, this isn’t at all reflective of the returns you could see investing in the financial markets, but it does help to understand how powerful compounding can be depending on the amount of money you’ve invested and the frequency at which compounding periods occur.

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compound interest

You can see from the table that progress is slow at the start. For example, it takes 15 days to get from 1p to over £160, but just 15 days after that to get to £5.4 million. So essentially, the more money you can keep in the markets instead of paying unnecessarily expensive fees, the better.

Taking advantage of compound interest could mean retiring earlier or with a better retirement income.

How can I start taking advantage of compound interest?

Here are five tips to make the most of compound interest on your investment portfolio.

1. Save up three months of outgoings and pay off expensive debt

Before you start investing, make sure you’ve paid off expensive debt and have three months of outgoings saved up in case of an emergency. This means that when you start investing, this money is ring-fenced for your future, so you can avoid dipping into it when you unexpectedly need cash. In addition, the more money you keep invested over the long term, the more you can benefit from compound interest.

2. Long time horizon

Perhaps the worst kept secret in personal finance, but the sooner you start saving and investing for your future, the better. A long-term time horizon allows you to take on more risk with your money, which increases your scope for higher returns and enables you to ride out short-term fluctuations in the value of your investments. This can make a real impact over the long run and could make all the difference to your pension income.  

3. Avoid expensive management fees and hidden charges

The more money you keep invested, the better compound interest works. When you’re paying expensive management fees for a service that isn’t performing as well as you’d like, you could be stifling your returns. The more you spend on fees, the less money you have working hard for you on the financial markets.

4. Set up a direct debit

Please don’t wait until you have a lump sum to start investing. The sooner you invest your money, the quicker it will work for you. Setting up a direct debit is a stress-free way to manage your investments, and you can ignore market noise when it comes to investing your money. You could also benefit from pound cost averaging, which can maximise your return by smoothing out the total amount you pay for an asset over time.

5. Reinvest everything

The amount of money you have invested and your time horizon are key when it comes to compound interest. By reinvesting any dividends or interest, you can get your money working harder and quicker, allowing you to reap the benefits of compounding.

Compound interest examples

Here are some compound interest future value examples that show annual, quarterly, monthly, and daily compounding using the formula.

 ​​A = P (1 + r / n) nt

Example 1. Annual compounding

Suppose John made an initial investment of £2,000 in 2020. What is the value of the investment after 5 years if the investment earns 10% interest compounded annually?

A = 2,000 * (1 + 0.10/1)(1*5)

A = 2,000 * (1 + 0.10)5

A = 2,000 * (1.10)5

A = 2,000 * 1.61

A = £3,221.02

Example 2. Quarterly compounding

Wex limited makes an initial investment of £12,000 for 20 years. What is the value of the investment after two years if the interest earned on the investment is  8% compounded quarterly?

A = 12,000 * (1 + 0.08/4)(4*20)

A = 12,000 * (1 + 0.02)80

A = 12,000 * (1.02)80

A = 12,000 * 4.875

A = £58,505.27

Example 3. Monthly compounding

Sam made an initial investment of £7,000. What is the value of the investment after 3 years if the investment earns 5% interest compounded monthly?

A = 7,000 * (1 + 0.05/12)(12*3)

A = 7,000 * (1 + 0.0042)36

A = 7,000 * (1.0042)36

A = 7,000 * 1.1614

A = £8,130.31

Example 3. Daily compounding

If Jessica invested £3,000 in 2010. After 12 years, she sold the investment for £4,500. What was the rate of return on investment if compounded daily?

4,500 = 3,000 * (1 + r/365)(365*12)

4,500 = 3,000 * (1 + r/365)4,380

4,500/3,000 = (1 + r/365)4,380

1.51/4,380 = (1 + r/365)

1.000092576 = 1 + r/365

1.000092576 – 1 = r/365

0.000092576*365 = r

r = 0.03379% or 0.034%

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FAQ

Can I get compound interest in the UK?

Yes, you can definitely get compound interest in the UK. All you need to do is make deposits into a UK compound interest savings or investment account and watch your money grow.

Where can I invest my money to get compound interest?

There are several places you can invest your money to get compound interest. Some of the best compound interest investments include certificates of deposit (CDs), high-yield savings accounts, bonds, money market accounts, dividend stocks and real estate investment trusts (REITs).

How to get compound interest in the UK?

To find the best compound interest account, first, research the interest rates offered on each financial product. Then, compare products from different providers because the interest rates can be calculated yearly, quarterly or monthly. The frequency of interest rate payments greatly affects the overall value of savings in the long term. Some of the most popular savings accounts that pay compound interest in the UK include ISAs, SIPPs, fixed bonds, and easy access accounts.

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