Compound interest : Explanation and examples
What is compound interest and how can I benefit from it?
hen it comes to finance, there are numerous ways to increase your wealth, notably through growing your investments. This is exemplified by compound interest, which Albert Einstein famously dubbed the "eighth wonder of the world."
But what exactly is compound interest? What purposes does it serve, and how can you benefit from it? From calculations and formulas to advantages and disadvantages, here is everything you need to know about the subject.
What is compound interest?
Unlike simple interest, which is calculated based on the original capital, compound interest is computed using a formula that combines the sum used for interest calculation with previously accrued interest.
In essence, its interest earned on money that has already generated interest, often referred to as "interest on interest." Consequently, an investor who engages in this financial method and refrains from withdrawing the invested money can achieve increasingly greater returns over time.
Simple and compound interest differ primarily in their calculation basis. Simple interest is calculated solely on the initial capital, whereas compound interest involves accruing additional interest at the end of each period (be it annual, monthly, or daily), which then gets added to the capital for the subsequent period. Typically, interest is compounded after it has been invested for more than a year. For periods less than a year, it is considered simple interest.
What is their use?
Compound interest can be used to multiply your assets. But how? Wealth grows from year to year without any intervention, mainly due to the compounding effect behind the increase in your savings.
In short, due to this effect, your money grows quickly and efficiently. You can even invest a small amount in an investment fund, and you'll see a higher return compared to the interest on your savings account.
Compound interest means that the money in your savings, i.e., your monthly or annual investments and start-up capital, gradually increases.
The very purpose of this special interest is to invest and reinvest over time, as new interest is earned and enhanced over time.
How to benefit from compound interest?
When you deposit your money in an account, you earn interest on it. If you do not withdraw the interest accrued, it will be added to the original amount for the next interest period. Consequently, each year you will receive more interest income than the previous year.
How to benefit from compound interest when rates are low?
In times of low interest rates, savings don't really pay off. In order to take advantage of compound interest during the low-rate period, you'll inevitably need to bank on investments.
How to invest in compound interest?
By initially investing a certain amount of money in assets like the stock market, real estate, or life insurance, your investment can grow significantly over the long term. This allows you to benefit from compound interest, even with smaller capital investments.
Compound interest calculation and formula
To explain compound interest in a simpler way, there's nothing better than using examples and calculations. To calculate compound interest, there are several formulas available :
Formula to calculate annual compound interest.
You need to use the following formula.
A=P⋅(1+n/r) n⋅t
Where :
- A is the final investment amount after a period of time t.
- P is the initial investment amount (CHF 200 in your example).
- r is the annual interest rate (expressed as a decimal). For example, if the interest rate is 5%, r=0.05.
- n is the number of times interest is capitalized per year (for example, annually, quarterly, monthly, etc.). For example, if interest is capitalized annually, n=1.
- t is the duration in years for which the investment is maintained.
Example of annual compound interest :
You decide to invest CHF 200 at an interest rate of 4% for 5 years. The resulting sum will be as follows: A=200⋅ (1+10.04)1⋅5 = 243.36 CHF
You'll earn CHF 43.36 in interest over 5 years.
Monthly compound interest formula
For a monthly calculation, you can use this formula :
Income amount = initial amount x (1+interest rate/interest period/100) ^(term x interest period).
The circumflex means power or exponent.
Example: If you invest CHF 200 at a rate of 4% for 2 years, with a monthly interest period of 12 months, the calculation will be as follows:
200 x (1+4/12/100) ^(2x12) = 221.83 CHF
The total investment after 2 years will have a final difference of CHF 221.83.
The formulas are the same for calculating daily compound interest. The figure to be changed if annual, monthly, or daily is the interest period:
- Annual: €1
- Quarterly: €4
- Monthly: 12
Good to note: the most commonly used formula for calculating compound interest is the first one listed: C0 (1+i) n = Cn.
In fact, compound interest is generally calculated on an annual basis.
What about investment interest?
It is calculated using the following formula:
Investment interest = initial amount - investment amount.
What is the 72 rules?
This rule was discovered by Albert Einstein. It's a calculation method which allows you to quickly estimate how long it shall take to double your initial investment.
It highlights the relatively large effect of compound interest on investments versus savings.
It's a simple formula that allows you to quickly calculate the number of years it will take to double your assets.
The figure 72 is divided by the average annual income. For savings, divide by the annual interest rate. For an investment, the number 72 is divided by the average annual yield.
This is how the formula is represented: 72/r = Y
- The "r" represents the compound annual interest rate or average annual return.
- “Y" represents the number of years required to double this investment.
For example, if the annual interest rate is 4%, we get this: 72/4 = 18 years.
It will then take 18 years to double the initial investment.
In the case of a savings account with an interest rate of 0.2%: 72/0.2 = 360 years.
This means that through savings, the investment will take 360 years to double.
In summary, the rule of 72 clearly demonstrates that savings accounts generate much less wealth (or hardly anything) compared to investments when compound interest is used.
With this rule of thumb, you'll quickly find out the approximate impact that compound interest will have on your initial investment.
Compound interest calculator
Feeling lost with all those formulas and calculations? Use an Excel spreadsheet and enter the right formula to calculate your taxed interest.
Is it still not clear? Choose your yield assumption and simulate the benefits of compound interest with our online graph. This table will allow you to observe the impact of compound interest.
Compound interest : pros and cons
The benefits have been primarily outlined throughout this article. In essence, they capitalize on the simple interest earned on your savings. As a result, your savings accrue a little more each year. In contrast, with simple interest, the amount received remains constant regardless of the number of years that pass.
Therefore, it's advisable to start saving as early as possible. The sooner you begin, the greater the compound interest you will accumulate. As an investor, this approach allows you to significantly increase your investment over time.
Higher profits, yes, but...
However, this 'snowball effect' can become costly in the context of credit. Some financial institutions charge interest not only on the initial amount but also on the accumulated interest charges. Consequently, the total repayment amount can increase rapidly, often exceeding the originally borrowed sum. This situation becomes even more burdensome if payments are delayed.
We also recommend against investing funds that you might need in the short term. Effective utilization of compound interest involves investing for several years without accessing the saved money. In cases of financial hardship, such an investment strategy is not advisable.
To learn more about the fundamentals of investing or to specialize, visit our academy.
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