how to calculate compound interest

The Wall Street Journal (WSJ) published an article a few years back,  a three-question test of financial literacy (which, of course, unleashed fury in the comments on financial literacy – or lack thereof – in North America.) But what I did notice was that while the WSJ provided the answers, no one took the time to explain why the answers are the answers

Which I think is not so great because if you didn’t get all or any of the answers right, you might feel not-very-smart and that’s not allowed here on The Money Coach.

There are no stupid questions, just an industry that is most profitable when financial literacy is not part of the equation.

Let’s do this! The first question was: 

1. Suppose you had $100 in a savings account, and the interest rate was 2% per year. After five years, how much do you think you would have in the account if you left the money to grow?

A. More than $102

B. Exactly $102

C. Less than $102

The answer to this lies in understanding the concept of compound interest. You can click that for the Wikipedia definition, but here is mine:

If you have $100 and put it in a savings account that pays 2% per year, at the end of the first year, you will have $102. (100 x 2% or 100 x 1.02 = 102). So that is after one year. The question asks how much you will have after five years. 

Working this out from day one: 

Year one: 102 x 1.02 = $102

Year two: 102 x 1.02 = $104.04

Year three: 104.04 x 1.02 = 106.12

Year four: 106.12 x 1.02 = 108.24

Year five: 108.24 x 1.02 = 110.40

After five years, you would have $110.40, which is more than $102. 

The answer is A.

If you break this down, the magic of compound interest is that not only does your original amount (in this case, $100) earn interest every year, but so does your year-on-year interest. In the second year, your $2.00 of interest (from the first year) also earns 2% interest. And then, in year three, your $4.04 is earning 2% interest, and you get the idea. 

A common (and understandable) mistake is to take the 2% per year and multiply by 5 (the five years in the question), which is 10%, and so $100 x 10% is $110. However, this is not correct. When your interest pays annually (once every year), your interest payment becomes part of your original amount (so at the end of year one, $100 because $102). And so, for each subsequent year, your new capital amount is higher than the year before.  

Got it?

Answers to questions two and three are here and here

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