# Power Of Compounding Interests Over Time If you have a lump sum of \$5,000 (and a choice to save \$1,200 per year) to save / invest today, do you know how much all these money would have grown across different Compounding Interest Rates (e.g. 0.05%, 1%, 3.5% & 7%) and Time Range (e.g. 10, 20 & 50 years)?

### But First, Understand What Is Compounding Interest…

In a simple way, Compounding Interest is the Interest you get to earn from your Interest and the process repeats.

And to explain this using a 3-year example, you have \$10,000 and a 1% compounding interest rate…

• At the end of Year 1, you will have earned \$100 (from the 1%). Your amount is now at \$10,100.
• At the end of Year 2 (assuming you never touch), you will have earned \$101 now (the \$1 is from the \$100 you have earned in Year 1), so your new amount is now at \$10,201.
• At end of Year 3, you will have a new total amount of \$10,303.01 which is calculated from 1.01% multiplied with \$10,201.

And if you add a monthly saving e.g. \$1200 per year, you will get interest from both the initial amount as well as the additional yearly amount.

### Calculators & Excel Formulas

#### — Calculators

One of the tools, that I have commonly used to illustrate the Power of Compounding Effects, is one that our (Singapore) CPF Board has provided. You can access this calculator tool by clicking here. Alternative site is the calculator from MoneyChimp.

#### — Excel Formula

If you like to see your numbers with Excel / Google Sheet, you can use this formula

=FV(Interest Rate , Number Of Periods , Payment Amount , Present Value , End/Beginning)

where

• FV is Future Value or the Calculated Amount, e.g. \$10,100 (after 1 year)
• Interest Rate, e.g. 1%
• Number Of Periods, e.g. 1 (to indicate 1 year)
• Payment Amount, e.g. 0 (to indicate no annual saving) or -1200 (to indicate annual saving of \$1,200)
• Present Value, e.g. 10,000 (initial amount)
• End or Beginning – i.e. 0 or 1. Default is 1 if you have an Annual Saving and you want this amount to be compounded.

If things are good so far, let’s look at how your \$5,000 (and \$1,200 per year) will grow across different Interest Rates and Years

### — Compounding Interest Rate Of 0.05% Per Annum

This is the interest rate that the local banks are giving you for your normal savings account with them:

For your lump sum of \$5,000:

If you decide to save \$1200 per year (or \$100 per month) on top of your initial lump sum of \$5,000…

### — Compounding Interest Rate Of 1% Per Annum

You can usually find this rate among investment channels like Fixed Deposits, Money Market Funds and Bonds.

For your lump sum of \$5,000:

If you decide to save \$1200 per year (or \$100 per month) on top of your initial lump sum of \$5,000…

### — Compounding Interest Rate Of 3.5% Per Annum

You can usually find this Interest Rate among channels like Traditional Endowment Plans from Insurance Companies, CPF Ordinary Account (2.5%), CPF Special Account (4%).

For your lump sum of \$5,000:

If you decide to save \$1200 per year (or \$100 per month) on top of your initial lump sum of \$5,000…

### — Compounding Interest Rate Of 7% Per Annum

You can find this interest among investment channels like Equities / Shares Investment. Tools like this come with some investment risks.

For your lump sum of \$5,000:

If you decide to save \$1200 per year (or \$100 per month) on top of your initial lump sum of \$5,000…

### Key Points To Take Note And A New Concept – Rule Of 72

#### — The Rule Of 72

If you have looked at the numbers closely, you would have noticed some of the amounts nearly doubled or have increased multiple times from the original amount. e.g. Compounding Interest Rate of 7% across 10 years gives \$9,835.76 – nearly double of \$5,000.

This is the Concept of the Rule of 72 where you can use it to calculate the number of years for an original amount to double. So for 7%, Years To Double = 72 / 7 = 10.3. From the example above, another 0.3 years (or 4 months later), the amount of \$5,000 would have doubled to \$10,000.

#### — Key Concepts

• Higher Compounding Interest Rate Per Annum gives a higher return compared to Lower Compounding Interest Rate Per Annum. So if you are currently saving your money in just a normal Bank Account, it’s time to venture out to look for something with higher interest rate and within your risk appetite.
• Compounding your Money over a longer period gives a higher return. If you see the numbers in the 50 years range for those higher interest rates, you would see the amount increased multiple times the original amount. So if you understand this well, you would want to start saving / investing earlier.
• In reality, Compounding Interest Rates that are high and offered by many of those investment tools out there are not constant throughout. Due to economic conditions, they can be high, low or even flat but if you ride through these over the years, you can average out the returns.

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