Albert Einstein once said, “Compound interest is the eighth wonder of the world. Whoever understands it, wins it. Whoever doesn’t, pays.

Compounding takes place when interest is calculated on both the original amount invested or borrowed (the “principal”) plus interest from previous years.

This differs from so-called “simple” interest, i.e. when interest from previous years is ignored and the calculation is made only with reference to the initial amount.

Understanding the difference between simple interest and compound interest can help you earn money as a saver or investor or lower the cost of any borrowing.

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

**simple interest** this is when the interest you earn or pay stays the same each year (if there is no change in the interest rate paid or charged, and the principal stays 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 earn interest on interest, or “compound” your returns.

An example illustrates the difference between simple interest and compound interest. You have £1,000 to invest at a fixed interest rate of 10% per annum. Here is the balance at the end of each year:

As shown in the table, interest of £100 is charged each year for the simple interest account (£1000 x 10% = £100 per year).

For compound interest, interest is paid on the closing balance at the end of the previous year, which includes interest paid in previous years. For example, second year interest is calculated as 10% of £1,100 instead of £1,000 as for simple interest.

After 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:

**Director:**the amount of money invested or borrowed, which is used to calculate interest. The principal can increase or decrease based on deposits or withdrawals.**Interest rate (or yield):**the higher the interest rate (or yield), the more money you will receive or pay. Interest rates can be fixed for a period of time or variable (subject to change).**Duration:**the length of time the money will be invested or borrowed, which may be a fixed or indefinite period. The longer the period, the higher the interest due to the power of compounding.**Dialing frequency:**interest can be compounded daily, monthly or annually. The more frequent the compounding, the faster the balance will increase.

It is also useful to understand the difference between APR, AER and APY:

**Annual percentage rate (APR):**it is the annual interest rate payable on mortgages, loans, credit cards and other simple interest borrowings. It includes any initial costs in addition to debit interest, spread over the term of the loan.**Equivalent Annual Rate (AER):**the interest or return earned on investments, taking into account the frequency with which interest is paid on a simple interest basis.**Annual Percentage Yield (APY):**the interest or return earned on investments on a compounded basis. It is a better indication of returns than the AER if you do not intend to make withdrawals.

For loans, you should keep in mind that you will end up paying an effective interest rate higher than the APR if interest is charged on a compounded basis and you are unable to make overpayments to compensate for this.

**What are the interest rates generally used?**

Ideally, you’d want to pay simple interest on loans and receive compound interest on investments, but that’s not always the case:

**Investments:**most investments, including savings accounts and stocks, are based on interest or compound returns. The exception is bonds and gilts, which pay simple interest, known as the coupon rate.**Loans:**simple interest is commonly used as the basis for personal loans, auto loans, and shorter-term forms of consumer loans. Credit cards and student loans use compound interest, which means debt can add up quickly if it’s not paid off.

Mortgages deserve a separate mention because they can be based on simple or compound interest:

**Traditional repayment mortgages**use compound interest, but the monthly payment and any overpayment reduce the outstanding balance or principal and, by extension, the interest payable.**Interest Only Mortgages**are based on simple interest which is charged monthly 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 make sure you don’t overpay for your loans:

**Choose simple interest loans:**you will pay less on a simple interest loan than on a compound interest agreement. For example, a personal loan charges simple interest, while a credit card charges compound interest.**Choose 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 prepayment, this may come with a one to two month interest charge. Some loans will allow you to overpay without penalty, reducing your interest costs.**Pay off more expensive debts:**you must first pay off the most expensive debt (the one with the highest compound rate), for example, credit cards before personal loans.

You can also use the power of compound returns to increase the value of your investments:

**Maximize your investment time:**the longer the time invested, the higher your income, because the capitalization will have more impact. For example, £10,000 earning a compound annual return of 8% would be worth almost £22,000 after 10 years, almost £47,000 after 20 years and over £100,000 after 30 years.**Use tax wraps to protect your earnings:**in the example above, you would have realized 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 exempt 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 the following year. For stocks, you can choose to have dividend payments automatically reinvested by purchasing additional stocks, rather than receiving cash dividends. For funds, you can choose to invest in ‘accumulation’ units rather than ‘income’ units, which use any income earned to buy additional units in the fund.

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**Increase in management fees**

The impact of compounding on fees should also be considered, as this can significantly erode the value of your portfolio.

Let’s look at an example based on the actual fee structures charged by three of the major trading platforms, using the same assumptions in each case:

**Platform 1**charges an annual fee of 0.45% based on the value of your portfolio (which is expected to 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 an annual fee of 0.25%, which means the portfolio grows to £133,000 after 20 years.**Platform three**charges a flat annual fee of £120 (assuming no increases over time) and your portfolio is worth £134,000 after 20 years.

The fee difference makes a substantial difference in the value of your portfolio over time due to the mix of returns and fees, although the difference may seem marginal.

You should research the best trading platform for your situation, as fees can vary widely.