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Compounding is a process where interest is credited, not only to the original ‘principal’ amount, but also to previously earned interest. This interest earned on interest results in the maximisation of returns over time.
This process differs from so-called ‘simple’ interest, which is when interest from previous years is ignored, and the calculation is made only with reference to the original amount.
Albert Einstein once said: “Compound interest is the eighth wonder of the world. He who understands it, earns it. He who doesn’t, pays it.”
We explain the difference between simple and compound interest so you have the best chance of making money as a saver or investor, or reducing the cost of any borrowing.
What is the difference between simple and compound interest?
Simple interest is when the interest you earn or pay stays the same each year (if there’s no change in the rate of interest paid or charged, and principal remains the same).
Compound interest is calculated on the gross balance at the end of the year, which includes any interest accrued in previous years. In other words, as a saver or investor, you’re earning interest on the interest, or ‘compounding’ your returns.
An example illustrates the difference between simple and compound interest. You have £1,000 to invest at a fixed interest rate of 10% per year. Here’s the balance at the end of each year:
As the table shows, interest of £100 is received each year for the simple interest account (£1,000 x 10% = £100 per year).
For compound interest, the interest is paid on the closing balance at the end of the previous year, which includes the interest paid in previous years. For example, the interest in year two is calculated as 10% of £1,100 rather than £1,000 as for simple interest.
By the end of 10 years, the balance is £2,000 for the simple interest account compared to £2,594 for the compound interest account.
Understanding compound interest calculations
There are a number of variables to consider when calculating compound interest, which can make a significant difference:
- Principal: the sum of money invested or borrowed, which is used to calculate the interest. The principal may increase or decrease depending on any deposits or withdrawals.
- Interest rate (or return): the higher the interest rate (or return), the more money you’ll receive or pay. Interest rates can be fixed for a period of time or variable (subject to change).
- Duration: the length of time for which the money will be invested or borrowed, which may be a fixed period or open-ended. The longer the period, the higher the interest due to the power of compounding.
- Frequency of compounding: interest can be compounded daily, monthly or annually. The more frequent the compounding, the more rapidly the balance will grow.
It’s also worth understanding the difference between APR, AER and APY:
- Annual Percentage Rate (APR): this is the annual rate of interest payable on mortgages, loans, credit cards and other borrowings on a simple interest basis. It includes any upfront fees in addition to the interest charge, spread over the duration of the loan.
- Annual Equivalent Rate (AER): the interest or return earned on investments, taking into account how often interest is paid on a simple interest basis.
- Annual Percentage Yield (APY): the interest or return earned on investments on a compound basis. This is a better indication of returns than AER if you do not intend to make any withdrawals.
For loans, you should bear in mind that you will end up paying a higher effective interest rate than the APR if the interest is charged on a compound basis and you are not able to make overpayments to offset this.
Which interest rates are typically used?
Ideally, you’d want to pay simple interest on loans and receive compound interest on investments, but this isn’t always the case:
- Investments: most investments, including savings accounts and equities, are based on compound interest or returns. The exception is bonds and gilts, which pay simple interest, known as the coupon rate.
- Borrowings: simple interest is commonly used as the basis for personal loans, car loans and shorter-term forms of consumer loans. Credit cards and student loans use compound interest, meaning that the debt can grow quickly if it’s not repaid.
Mortgages are worth a separate mention as they can be based on simple or compound interest:
- Traditional repayment mortgages use compound interest, but the monthly payment and any over-payments reduce the outstanding balance or principal, and by extension, the interest payable.
- Interest-only mortgages are based on simple interest which is charged on a monthly basis on the amount borrowed (the principal must be repaid separately as a lump-sum at the end of the mortgage term).
How to make compound interest work for you
There are steps you can take to ensure you’re not over-paying for borrowings:
- Choose simple interest loans: you’ll pay less on a simple interest loan than on a compound interest deal. For example, a personal loan charges simple interest, while a credit card charges compound interest.
- Picking low interest rate options: according to the Bank of England, the average interest rate on credit cards is 19% compared to 7% for personal loans.
- Look for flexible loans: although personal loan providers are legally required to allow early repayment, this can come with a fee of one to two months’ interest. Some loans will allow you to make overpayments without penalty, which will reduce your interest cost.
- Pay down more expensive debt: you should repay the most expensive debt (that with the highest compound rate) first, for example, credit cards before personal loans.
You can also use the power of compound returns to boost the value of your investments:
- Maximise your investment period: the longer the time invested, the higher your earnings as compounding will have more of an impact. For example, £10,000 earning a compound annual return of 8% would be worth almost £22,000 after 10 years, nearly £47,000 after 20 years and over £100,000 after 30 years.
- Use tax wrappers to shield your gains: in the example above, you would have made a capital gain of £90,000 after 30 years, which would be subject to capital gains tax of up to 20%. However, investments held in an Individual Savings Account (ISA), Self Invested Personal Pension (SIPP) and Junior ISA are free from capital gains tax (and income tax).
- Reinvest dividends or income: for a savings account, leaving rather than withdrawing the interest allows you to benefit from compound interest in the next year. For shares, you can choose to automatically reinvest dividend payments by buying additional shares, rather than receiving dividends in cash. For funds, you can choose to invest in ‘accumulation’ rather than ‘income’ units, which use any income earned to buy additional units in the fund.
Compounding on management fees
The impact of compounding on fees should also be considered as this can significantly erode the value of your portfolio.
Let’s take a look at an example based on actual fee structures charged by three of the major trading platforms, using the same assumptions in each case:
- Platform 1 charges a 0.45% annual fee based on the value of your portfolio (which should grow over time). You invest £30,000 for 20 years with an annual return of 8%. At the end of this period, your portfolio is worth £128,000.
- Platform two charges a 0.25% annual fee, meaning that the portfolio increases to £133,000 after 20 years.
- Platform three charges a flat £120 annual fee (assuming no increase over time) and your portfolio is worth £134,000 at the end of 20 years.
The difference in fees makes a substantial difference to the value of your portfolio over time due to compounding of the returns and the fees, even though the difference may seem marginal.
You should look for the best trading platform for your circumstances as fees can vary significantly.
