How to Learn the Difference Between Simple Interest and Compound Interest

This Article will show by an Example Problem How to Know the Difference Between Finding the Simple Interest and Finding the Compound Interest, on a Given amount of Money Invested, for a Given Time, at a Given Rate. Summarizing with two Formulas, one Formula for the Simple Interest and one Formula for the Compound Interest.

Things You'll Need

• Paper
• Pencil and a
• Scientific Calculator

Instructions

1. 

   The Example Problem is: Find the Difference Between the Simple Interest and the Compound Interest on an Investment of $1000,(Called Principal or Capital), for 3 years,(Time), at 5% annually,(Rate). We will First go through the process of finding the Amount of Interest at the end of each year, then we will take the Total of these Interests. Please Click on Image for a Better Understanding.

2. 

   At The end of the First Year, The Simple Interest on $1000 @ the rate of 5% is : $1000 x 5% = $1000 x 0.05 =$50. At the end of the Second Year, the Interest is : $1000 x 0.05 = $50. At the end of the Third Year, the Interest is : $1000 x 0.05 = $50. The total Simple Interest for the 3 years is $150. Please Click on Image for a Better Understanding.

3. 

   This Process is OK for 3,4,or 5 years but will be tedious for 30,40,50 years or more, so a Simple Formula will be Welcomed at this time. the Formula is: Simple Interest = Principal x Time x Rate/100%. That is the Simple Interest = $1000 x 3 x 5%/100% = $1000 x 3 x 0.05 = $150. Please Click on Image for a Better Understanding.

4. 

   We now turn our attention to finding the Compound Interest for the same Given Problem. At the end of the First Year,The Compound Interest on $1000 @ the rate of 5% is : $1000 x 5% = $1000 x 0.05 =$50. We now Add this Interest of $50 to the Principal of $1000, giving us The Total of $1050 to be invested for the Second Year. Please Click on Image for a Better Understanding.

5. 

   At the end of the Second Year the Compound Interest on $1050 at the rate of 5% is : $1050 x 5% = 1050 x 0.05 = $52.50, we Add This Interest of $52.50 to the Principal of $1050, giving us the Total of $1102.50 to be invested for the Third Year. Please Click on Image for a Better Understanding.

6. 

   At the end of the Third Year the Compound Interest on $1102.50 at the rate of 5% is : $1102.50 x 5% = 1102.50 x 0.05 = $55.125, we Now Add all the Compound Interests for the 3 years, giving us the Total of
   $50 + $52.50 + $55.125 = $157.625, rounding off this Amount to the nearest hundredth, we get $157.63 as the total Compound Interest. Please Click on Image for a Better Understanding.

7. 

   Again we can see that this process would be very Tedious and Time consuming, so a Formula that would make it much easier to calculate the Compound Interest will be greatly appreciated at this time.
   The Formula for the Compound Interest is : Compound Interest = Principal x ( 1 + Rate/N )^ (N x Time) - Principal, where N is the Number of times within one year that the Principal should be reinvested. Please Click on Image for a Better Understanding.

8. 

   Using The Compound Interest Formula with the above Given Problem we get the following: Compound Interest = $1000 x (1 + 0.05/1)^(1x3)-$1000 =
   $1000 x (1 + 0.05)^3-$1000 = $1000 x 1.05^3-$1000 = $1000 x 1.157625-$1000 = $1157.625 - $1000 = $157.625, which is approximately $157.63. Please Click on Image for a Better Understanding.

9. 

   The Difference Between The Compound Interest and Simple Interest of the Given Problem above is, $157.63 - $150 = $7.63. Please Click on Image for a Better Understanding.