Simple vs compound interest (tutorial #12)

After discussing why we care about interest rates, we move on to explaining the difference between simple  interest and compound interest. Suppose that you would like to deposit $10,000 into a bank account for 10 years. Bank Simple offers a simple interest rate of 11% per year, whereas Bancompound offers a compound interest rate of 10% per year. Which bank should you deposit with?

Let's first analyze Bank Simple's offer. If you deposit with this bank, at the end of the first year, you will earn an interest of 11% ($10,000) = $1,100. That means your deposit will grow to $11,100. How about the second year? You will again earn an interest of 11% ($10,000) = $1,100. Why is that? This is because, even though your deposit is worth $11,100 in the second year, Bank Simple pays interest only on your principal, which is $10,000. This is what we mean by simple interest: You earn interest only on your principal. 

Now, let's turn to Bancompound's offer. If you choose this bank, the interest you earn in one year will be 10% ($10,000) = $1,000, and your deposit will grow to $11,000, which is smaller than what you would have with Bank Simple. In the second year, though, you will earn an interest of 10% ($11,000) = $1,100. In other words, Bancompound pays interest not only on your principal, which is $10,000, but also on the interest you earned so far, which is $1,000. And, this is what we mean by compound interest: You earn interest not only on your principal, but also on the interest you earned in the past.

We still didn't answer the question about which bank you should deposit it. To answer that, we should find out which bank account yields the highest value at the end of 10 years. If you deposit with Bank Simple, you will earn an interest of $1,100 each year. This means that after 10 years, the value of your deposit will be:  $10,000 + 10 ($1,100) = $21,000. On the other hand, if you deposit with Bancompound, after 1 year, the value of your deposit will grow to:

$10,000 + 10% ($10,000) = (1 + 10%) $10,000 = $11,000

After 2 years, it will grow to:

$11,000 + 10% ($11,000) = (1 + 10%) $11,000
= (1 + 10%) (1 + 10%) $10,000 = (1 + 10%)² $10,000 

And, after 10 years, its value will be:

(1 + 10%)¹⁰ $10,000 = $25,937.42

Therefore, you are much better off depositing with Bancompound, since $25,937.42 > $21,000, even though the rate offered by Bank Simple is higher (11% > 10%). This is because, Bancompound pays compound interest whereas Bank Simple pays simple interest.

The figure above compares the growth of your $10,000 deposit in Bank Simple and Bancompound. For the first 3 years, the growth rates are more or less the same, but after the 3rd year, your deposit starts growing faster and faster in Bancompound due to the fact that this bank offers compound interest. At the end of 10 years, your deposit grows almost to $26,000 in Bancompound, but it remains below $22,000 in Bank Simple.

This simple example illustrates the power of compounding. Banks normally offer compound interest to their customers. In fact, many bank accounts compound interest more than once a year. For instance, you can have a bank account that pays compounded interest monthly. The compounding frequency is the topic of the next tutorial.

Next tutorial: Compounding frequency
Previous tutorial: Why do we care about interest rates?

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