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In everyday life we often hear phrases like “interest on interest” or “interest that breeds interest”. These are typical ways of describing one method of calculating interest: “compound interest”. And where there is compound, there is usually simple too! So what exactly are simple interest and compound interest? Let’s find out with Green Chart in the article below.
What Is Simple Interest?
Simple interest is the most common way of calculating interest. Put simply, it is the amount paid or received over a given period as a fixed percentage of the principal borrowed or lent.
Simple interest is calculated with the formula: Simple interest = P × i × n
Where:
P = the principal
i = the annual interest rate (%)
n = the loan term, in years
Example: A borrows VND 100 million from B. They agree on a 5-year term at an annual interest rate of 10%, paid as simple interest.
The total interest the borrower must pay over 5 years is then: 10% x 100 million x 5 = 10 million x 5 = VND 50 million.
This is the simplest way to calculate interest, but in practice, if the lender wants a higher return rather than the same interest every year, simple interest is no longer the best choice. Instead, the lender can opt for compound interest, the most familiar example being bank term deposits. So:
What Is Compound Interest?
Compound interest is interest calculated on a base that includes the interest from earlier periods, which is added to the principal and used to calculate the interest for the following periods.
Compound interest is calculated with the formula: P x (1 + R)n
Where:
- P = the principal
- R = the interest rate per period
- n = the number of compounding periods
Why is compound interest calculated this way? Take the same VND 100 million loan from B to A over 5 years at 10% a year, but this time B wants interest calculated on a compound basis. The interest A must pay each period (year) is:
Interest in year 1 = 10% x 100 million = VND 10 million
Interest in year 2 = 10% x (100 million + 10 million) = 11 million
Interest in year 3 = 10% x (100 million + 10 million + 11 million) = 12.1 million
Interest in year 4 = 10% x (100 million + 10 million + 11 million + 12.1 million) = 13.31 million
Interest in year 5 = 10% x (100 million + 10 million + 11 million + 12.1 million + 13.31 million) = 14.641 million
So after 5 years, the total interest A pays B (or B receives) is VND 61.051 million. Including principal, B receives 100,000,000 + 61,051,000 = VND 161,051,000, which is exactly the result of applying the compound interest formula above:
100,000,000 x (1 + 10%)5
= VND 161,051,000
As you can see, from the borrower’s point of view, borrowing at simple interest lightens the interest burden; conversely, lenders prefer to lend at compound interest because it brings a higher return, with interest growing faster in each new cycle.
The Compounding Effect
The physicist Albert Einstein is said to have described compound interest as the eighth wonder of the world. In finance, compound interest or compound returns refers to the ability of money to grow when the profit from year 1 is reinvested in year 2, the profit from year 2 is reinvested in year 3, and so on.
Example: imagine you invest VND 100,000,000, expected to grow at 20% a year (this is also called the CAGR, or simply the growth rate). At the end of the first year, it has grown to VND 120,000,000.
At the end of year 1, you have two options:
- Leave the VND 20,000,000 profit invested along with the original VND 100,000,000 principal, or
- Withdraw the VND 20,000,000 profit.
You decide not to withdraw the VND 20,000,000 profit; instead, you reinvest it for year 2. At the end of year 2, the 120,000,000 grows 20% to VND 144,000,000. At the end of year 3, the VND 144,000,000 grows 20% to 173,000,000, and so on…
Compare this with withdrawing the VND 20,000,000 profit every year. If you withdrew 20,000,000 each year, your total profit at the end of year 3 would be VND 60,000,000.
But because you stayed invested, your profit after 3 years is VND 73,000,000. That is VND 13,000,000 more, or 21.7% more than the VND 60,000,000 you would have earned by withdrawing the profit every year instead of staying invested.
This is called the compounding effect.
Let’s dig a little deeper and look at the chart below:
The compounding effect
The chart above shows how VND 100,000,000 invested at 20% grows over 10 years.
Factors That Affect Compounding
Compound interest and the size of its effect depend on a few key factors:
Time: time is arguably the most important factor for deposits earning compound interest. In the early years, the interest earned is not much different from simple interest. But over long periods (10 years or more), compounding really starts to make a big difference to our wealth. The basic rule is that the more compounding periods, the larger the compound interest.
Principal: the principal also plays an important role. Obviously, the larger the principal, the larger the interest. Combined with compounding, this increases the holder’s ability to grow their wealth.
Interest rate: as with the principal, the higher the interest rate, the more interest the depositor receives. The essence of compounding is reinvesting the interest you receive by adding it to your capital, so higher interest means faster growth in later periods.
Compounding frequency: depositors and borrowers can agree on the intervals at which interest is added to principal: daily, monthly, quarterly or yearly. Interest grows more steadily when it is compounded at regular, frequent intervals, which brings larger returns in the future.
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