*Interest rate*. We save to earn it. We grudgingly pay it on our housing loans. We depend on it in our retirement. As financial concepts go, there are few concepts more universal than interest rate. Yet, the concept and computation of interest rate confuses many people. Consider these two statements: (1) interest on your savings balance is calculated daily and compounded monthly, (2) interest on your savings balance is calculated daily but compounded and credited annually. Both statements are correct, depending on the context.

To illustrate what the first statement means, suppose you start the year with $10,000 in your account. Assume the interest rate is 1% per annum. What will be your balance at the end of the year assuming you did not withdraw any money? Answer: $10,100.46. Getting this answer is easy. Ignore the part about interest being calculated daily. What matters to you how is often is interest compounded. Since the bank says interest is compounded monthly, take 1+ 1% divided by 12 and multiply this factor by $10,000. In other words, (1+ 0.01/12) x 10,000 = $10,100.46.

Monthly compounding means that interest earned last month will earn interest this month, and interest earned this month will earn interest next month and so forth. That’s not so difficult to visualize. Just imagine a snowball growing bigger as it gathers snow while on its way down a slope. Compounding has this snowballing effect.

The opposite of compounding is “simple interest”. So, if your account pays a simple rate of 1% per annum, after a year, your balance will be $10,100 and not $10,100.46.

The second statement says that interest is compounded annually. Therefore, assuming that interest rate is a constant 1% per annum, your $10,000 balance will grow to $10,100 after one year, and $10,201 after two years. That is, 10,000 x 1.01^{2 }= 10,201.

Now for some useful facts:

- Bank savings accounts in Singapore pay monthly compounded interest.
- Fixed or time deposit accounts pay simple interest.
- Interests on all CPF accounts are compounded annually.

Before I end this blog, I should point out that the amount of wealth you accumulate through savings depends not only on the interest rate but also the amount saved over time. The more you save each month or year, the greater will be the effect of compounding on your ending balance. For example, assume you save $1,000 every month for 10 years. If interest is compounded monthly, interest is earned on interest over 120 times (because there are 120 months over a 10-year period). But if interest is compounded annually, interest is earned on interest only 10 times. Based on an interest rate of 1% per annum in both cases, your balance will be $126,149.88 under monthly compounding and only $125,546.55 under annual compounding (you can use excel to check these results). Unlike the one-year example above, the difference in balance is now an eye-catching $603. Not bad..provided you can muster the discipline to sock away $1,000 a month.