Compound Interest Explained for Dummies

What is compound interest?  

Compound interest refers to the interest calculated on the principal amount (initial amount) of a loan or deposit as well as on the accumulated past interest from the commencement date of the loan or the date of deposit.  Compound interest is commonly referred to as ‘interest on interest,’ implying it is interest earned on money that was already earned as interest.  The effect of compound interest can be compared with the ‘snowball effect,’ where a snowball starts small, but increases in size when more snow is added. As the snow accumulates, the snowball becomes bigger at a faster and faster rate.   

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The importance of understanding compound interest 

Albert Einstein (1879 - 1955), the world-famous physicist, who was named ‘Person of the Century’ (20th century) by Time magazine, referred to compound interest as the ‘eighth wonder of the world,’ saying: ‘He who understands it, earns it … he who doesn’t … pays it.’  Benjamin Franklin (1706 - 1790), one of the foremost Founding Fathers of the United States of America (USA), defined compound interest as follows: ‘Money makes money. And the money that money makes, makes money.’   In the above quotes, both Einstein and Franklin confirm the importance of the concept of compound interest. Understanding and applying compound interest allows you to increase your wealth. Conversely, ignoring compound interest will let you pay, losing opportunities to grow your health.  Put differently, compound interest enables an investor to earn interest from the original principal amount plus interest on the accumulated interest past interest.   Contrarily, a borrower of money will be obliged to pay interest on the original amount of the loan as well as on the interest that exists from previous periods. For instance, compound interest may occur when interest due is not paid by the specified date.  Compound interest is a commonly used concept in the financial world. Hence, investors and borrowers must make sure that they are acquainted with the concept.   

How to calculate compound interest 

• Formula and examples 

To calculate compound interest on investments or loans, the following formula can be used:  X = P (1 + r/n)nt - P   Where:  X = compound interest  P = principal amount (original amount)  r = annual interest rate (expressed in decimal form)  n = the number of compounding periods per unit of time. For example, annually is 1, semi-annually is 2, quarterly is 4, monthly is 12, and weekly is 52.  t = the number of time units the principal amount is invested or borrowed for. Differently put, it is the amount of time (expressed in years) through which the money compounds.    Example #1 (Interest compounded quarterly)  Let us say an investor deposits R10 000 into a savings account at an annual interest rate of 8%, compounded on a quarterly basis, for a period of 5 years.  X = P (1 + r/n)nt - P   X = 10 000 (1 + 0.08/4)4x5 - 10 000   X = 10 000 (1.02)20 - 10 000  X = 10 000 (1.485947) - 10 000  X = 14 859 - 10 000  X = 4 859  This means the amount in the savings account would grow from R10 000 to R14 859 with the cumulative interest (addition of all interest payments) over the period of 5 years.    Example #2 (Interest compounded monthly)  When the amount and investment period remain the same as in example 1, but the interest is compounded monthly, the calculation will look as follows:  X = P (1 + r/n)nt - P   X = 10 000 (1 + 0.08/12)12x5 - 10 000   X = 10 000 (1.006667)60 - 10 000  X = 10 000 (1.489875) - 10 000  X = 14 899 - 10 000  X = 4 899    Example #3 (Interest compounded annually)  When the amount and investment period remain the same as in examples 1 and 2, but the interest is compounded annually, the calculation will look as follows:  X = P (1 + r/n)nt - P   X = 10 000 (1 + 0.08/1)1x5 - 10 000   X = 10 000 (1.08)5 - 10 000  X = 10 000 (1.146932) - 10 000  X = 11 469 - 10 000  X = 1 469   

• Frequent compounding of interest 

In example #3 (compounded annually), the compound interest is lower than the compound interest in examples 1 and 2: R3 430 lower than the amount in example #2 (compounded monthly), and R3 390 lower than the interest in example #1 (compounded quarterly). This indicates that the frequency of compounding is notably important regarding calculations of compound interest - the more the number of compounding periods, the higher the compound interest.  When the period for an investment or loan is one year, the formulas for the different number of compounding periods will look as follow: 

• Annually compounding: P (1 + r) 

• Bi-annually compounding: P (1 + r/2)2  

• Quarterly compounding: P (1 + r/4)4 

• Monthly compounding: P (1 + r/12)12 

There are numerous online calculators available to assist you when calculating compound interest.   

• Compound interest table 

A compound interest table may help to understand how compound interest works. Say an investor invests an amount of R15 000 at an interest rate of 7% for a period of 5 years. The interest table will look as follows: 

Year	Investment at start of year	Interest (7% pa)	Investment at end of year
1	R15 000.00	R 1 050.00	R16 050.00
2	R16 050.00	R 1 123.50	R17 173.50
3	R17 173.50	R1 202.15	R18 375.65
4	R18 375.65	R 1 286.30	R19 661.95
5	R19 661.95	R1 376.34	R21 038.29

       The total compound interest earned is R6 038.29.     

What is simple interest? 

Simple interest refers to the interest calculated on the principal amount of a deposit or loan at a specified rate over a specific period. The interest calculation does not include compound interest.  The formula to calculate simple interest is:  Simple interest = P x r x n  Where:   P = Principal amount (original amount)  r = Annual interest rate  n = Term of loan/deposit (in years)  Example:  Let us take the same information used in the compound interest table above.  The simple interest on the investment of R15 000 will be calculated as follows:   P x r x n  = R15 000 x 0.07 x 5  = R5 250  The simple interest of R5 250 is R788.29 less than the compound interest earned on the investment.     

Rule of 72 

The Rule of 72 enables you to quickly estimate compound interest, allowing you to roughly determine how long it will take to double your investment by considering the interest rate and the length of the period you will earn that rate.  Buy Side from the Wall Street Journal (WSJ) defines the rule as follows: ‘The rule of 72 is a mathematical formula you can use to calculate how long it will take for an investment to double in value, presuming it has a steady annual rate of return,’ adding, ‘the rule is an easy-to-remember calculation.’ (Accentuation by the article writer.)   Apply the rule by simply dividing 72 by the annual rate of return.  Example:  If an investment has an expected annual rate of return of 8%, that means it can be expected to double in 9 (72/8) years. Likewise, if an investment has an expected rate of return of 6%, the expectation is that it can double in 12 (72/6) years.   Furthermore, rule 72 can also be used to determine what rate you must earn at a minimum to double your money over a certain period.   Example:  You want to invest R5 000, and you want R10 000 in return in 10 years. Divide 72 by 10, which equals 7.2. Hence, you will need to earn an annual rate of return of 7.2% to reach your investment goal.   

The power of compound interest 

Albert Einstein referred to compound interest as ‘the strongest force in the universe.’ Robert Breault (born 1963), a famous American tenor known for his inspiring quotes, also referred to the universe when describing the power of compound interest, saying: ‘If you understand compound interest, you understand the universe.’  Several factors make compound interest powerful. Factors such as time, frequency, and the interest rate applied. 

• Time 

Warren Buffet (born 1930), one of the most successful investors of all time, described the importance of time, offering the following advice: ‘Time is your friend, impulse is your enemy. Take advantage of compound interest and don’t be captivated by the siren song of the market.’  Compound interest grows money exponentially over time. Hence the longer an investment is left untouched, the more it can grow.  Compounding is more powerful (even breathtaking) over long periods.   Compound interest enables young people to make effective use of the time value of money (TVM), which is a core financial principle, stating that a sum of money is worth more now than in the future.  Always keep in mind when choosing investments that the number of compounding periods is equally important as the interest rate. 

• Frequency 

The fundamental rule of compound interest is that the higher the number of compounding periods, the greater the amount of compound interest. For example, weekly periods have more dramatic results than monthly periods, while monthly periods provide more impressive results than quarterly periods.   For instance, when starting a savings account, try to find an account that has the highest compounding periods, preferably daily.  

• Interest rate 

Higher interest rates will allow an account to grow more rapidly. However, compound interest can be at a lower rate. Over long periods, an investment compounding at a lower interest rate can outperform an investment using a higher simple interest rate.   

Advantages of compound interest 

• Understanding how compound interest works enables investors and borrowers to make informed decisions about investments and loans. 
• It reduces wealth-eroding factors such as the rising cost of living caused by inflation, as well as purchasing power reduced by inflation. 
• Compound interest is a key factor in building and increasing wealth because returns generate returns. 
• Compounding can work to a borrower’s advantage when making loan repayments. When a borrower pays more than his/her minimum repayment, he/she can leverage the power of compounding to save on total interest payments. 

 

Disadvantages of compound interest 

• Compound interest may be challenging to calculate, and you may need an online calculator. On the contrary, it is easy to calculate simple interest. 
• Compounding works against borrowers of money, favouring lenders instead. If a borrower only pays the minimum repayment required, the balance of the loan could continue growing dramatically because of compounding interest.  

 

Some more interesting compound interest quotes 

• ‘My wealth has come from a combination of living in America, some lucky genes, and compound interest.’ (Warren Buffet) 
• ‘Understanding both the power of compound interest and the difficulty of getting it is the heart and soul of understanding a lot of things.’ (Charlie Munger)  

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