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Simple vs. compound interest

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Focus on Finance by Anthony Conder

Question: What is the difference between simple and compound interest?

Answer: Whether you are investing or borrowing money you will more than likely have to deal with some form of interest. Your decision on how to invest or how to borrow should include a basic understanding on the difference of each and the impact they can have on your savings or debt. 

For example, let’s say you have $500 you want to invest. After calling around you find Bank A offering 10 percent simple interest for 10 years and Bank B is offering 7.5 percent compounded annually for 10 years. Which is the better deal?

Simple Interest. Simple interest is a very basic way of looking at interest and will give just a general idea on what the total amount of the loan or the investment will be in the end. It is the easiest type of interest to calculate and understand as it does not take compounding into consideration.

The formula for calculating simple interest is: I=Prt

Which means (I) the interest is calculated by multiplying Principal (P) times the rate (r) times the number of (t) time periods.

So given the example we have above the total amount of interest earned at Bank A would be:

I = ($500 initial investment) (10 percent rate of return) (10 year time period) or $500.

When you add that back to your original investment of $500, the total you would have after 10 years would be $1,000.

Because the simple interest method is calculated only on the original loan or investment amount, it generally is used for shorter-term loans and investments with terms less than 90 days.

Compound Interest. The difference between compound interest and simple interest is that with compound the interest being paid is added to the account during the specified time period. When the interest is added to the account it earns more interest because it has a higher balance. The more often interest compounds, the greater the difference between the simple and the compound interest will be. This assumes you will leave the money alone and allow it to compound.

The compound interest formula is significantly longer because the account accrues not only on the interest on the original amount but also interest on the interest added to the account. Therefore, being able to calculate compound interest means you must know the annual interest rate, compounding frequency, the amount of time interest accrues and the amount of money on which interest accrues.

The formula for calculating compound interest is as follows:

FV = P (1 + r / n) YN

FV = Future Value

P = Principal investment

r = interest rate

N = number of times interest is compounded per year

Y = number of years invested

So given the example we have above the total amount of interest earned at Bank B would be

FV = $500 (1 + 10 percent/1)(1x10)

Restated, FV = 500(1 + .10/1)10

FV = $1,296.87

Now that we have a better understanding of the difference between simple and compound interest we find that even though Bank A is paying a better rate of return, the best deal in the long run is Bank B.

Significance. The larger the dollar amount invested or borrowed, the greater the significance of the interest calculation method used. For example, if you only are borrowing $100 for a month or two, the difference will not be great. However, if you are taking out a car loan or mortgage, or putting aside money for retirement, making sure you use the proper interest formula will make a big difference. If you are borrowing money, compound interest means you need to budget for paying more interest. If you are saving money, you will end up with a higher ending balance than you would have otherwise had with simple interest.

Anthony Conder is assistant vice president and banking center manager at The Cecilian Bank.

 

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