Interest rates (calculating APRs, etc.)

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April 16th, 2006

The concept on which almost all of the financial world is interest and interest rates. Understanding how they work, and how they relate to your investments is key to taking control of your personal finances.

What is interest?
As a general rule, interest is defined as the value of money over time. What this means is that if Person A loans money to Person B, he must place some value on the money he is loaning out. After all, if the money were still in his possession during the term of the loan, he could be using it for other things, such as investments.

What is an APR?
APR stands for “Annual Percentage Rate” which is the extrapolation of an interest rate to the period of one year. Generally speaking, the true APR will be greater than the stated rate. For instance, if you have a bank account with “nominal” or “stated” rate of 3%, and your interest is calculated monthly, you are actually receiving 3.04% APR.

The difference between APR and nominal rates is very important, especially when considering large investments such as houses or cars.

How can I calculate the monthly interest rate?
Let’s take the example of a credit card with a 12% APR. If you are carrying a balance of $100 on it, how much interest will you be charged this month?

The easiest way to approximate this figure is to take the APR divided by the number periods in a year, and multiply with the balance.

What does ‘compound interest’ mean?
Compound interest occurs when money you earn is reinvested. The most common example of this strategy is with a typical savings account.

If you invest $100 in a savings account at 3.5% APR, then in one year’s time you will have $103.50. But, the bank doesn’t mail you a check for $3.50, they credit the money to your account. If you leave that money in the account for another year, you gain interest not only on your original $100, but also the additional $3.50.

As an example of how much faster compound interest grows vs. non-compound, take a look at this table:

Non-Compound Compound
Year 1 $ 103.50 $ 103.50
Year 2 $ 107.00 $ 107.12
Year 3 $ 110.50 $ 110.87
Year 4 $ 114.00 $ 114.75
Year 5 $ 117.50 $ 118.77
Year 6 $ 121.00 $ 122.93
Year 7 $ 124.50 $ 127.23
Year 8 $ 128.00 $ 131.68
Year 9 $ 131.50 $ 136.29
Year 10 $ 135.00 $ 141.06
Year 11 $ 138.50 $ 146.00
Year 12 $ 142.00 $ 151.11
Year 13 $ 145.50 $ 156.40
Year 14 $ 149.00 $ 161.87
Year 15 $ 152.54 $ 167.53
Year 16 $ 156.11 $ 173.40
Year 17 $ 159.71 $ 179.47
Year 18 $ 163.35 $ 185.75
Year 19 $ 167.03 $ 192.25
Year 20 $ 170.74 $ 198.98

So after 20 years, you will have almost $30 more in interest when your money is compounded.

There are, of course, more exciting applications of this concept, but this is a basic example.

Entry Filed under: Finance Principles
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