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Compound Interest: Why It Matters To You As An Investor

It is hardly an overstatement to say compound interest is the foundation of finance and capital markets. This article is an introduction to understanding this fundamental concept.

Interest is a return on an asset or the cost of capital. Assume we deposit $1,000 into a bank at an interest rate of 10% per annum. The bank tells us interest will be compounded on an annual basis. After one year, we will have earned 10% interest on our deposit. The interest will be $100 ($1,000 * (10/100)) and we will now have $1,100.

After two years, we will again earn 10% interest on $1,100. This will be $110 ($1,100 * (10/100)). We will now have $1,210.

What we are doing is to multiply $1,000 by 1.1 when the interest rate is 10%.

After one year, the final amount is $1,000 * 1.1

In two years, it is $1,000 *1.1*1.1

In three years, it is $1,000 *1.1*1.1*1.1

In year n, where n is the number of years, the final amount would be $1,000 * 1.1^n (1.1 to the power of n)

Now, what happens when the bank tells us interest will be compounded on a monthly basis on an interest rate of 10% per annum?

After one month, we will earn an interest of 10% divided by 12 months or 0.83% on our $1,000 deposit. This is equivalent to $8.33. We will now have $1,008.33.

After one month, $1,000 * 1.0083 = $1,008.33

After two months, $1,000 * 1.0083 * 1.0083 = $1,016.67

After six months, $1,000 * 1.0083^6 = $1,050.84

After one year or 12 months, $1,000 * 1.0083^12 = $1,104.27

Now the annual interest rate of both deposits are the same – 10%. But the rate of compounding is different. Compounding on a monthly basis means a higher effective interest rate as compared to compounding on an annual basis. Under monthly compounding, at the end of one year, we receive $104.27 in interest, or $4.27 more than annual compounding.

The frequency of compounding (years, months or days) is the difference between what is known as an annual interest rate from what is the effective interest rate. The annual interest rate of our deposit is 10%. However, on a monthly compounding basis, the effective interest rate is 10.4%.

In Singapore, our savings account are generally compounded on a daily basis. Just imagine, it is very difficult trying to calculate all those numbers in your head. Now a difference of 0.4% annually may not seem like a large amount of money, but imagine having to service a 20-year property loan worth $500,000. Things would add up very very quickly.

How do we apply compounding on a more practical basis? A useful shortcut to think about compound interest is the Rule of 72, which tells us how long it will take for us to double our money.

If we have a deposit of $1,000 and an effective interest rate of 3%, how long will it take for us to double our investment to $2,000? What we can do is to simply divide 72 by 3. This gives a quick approximation that we will need 24 years to double our investment.

If we could invest our money at much higher rates of return, we need a lesser number of years to double our money. This is why Albert Einstein is said to have referred to compound interest as the most powerful force in the universe.

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The information provided is for general information purposes only and is not intended to be personalised investment or financial advice.