How To Solve For Compound Interest
Many students run away from questions involving compound interests. This is often because they do not know the rules and guidelines to be taken when solving for the compound interest. Unlike simple interest, compound interest is a bit more complex to solve but if you follow the rules, you can deal with it comfortably.
In this article, I am going to give you detailed step-by-step guidelines on how you can solve questions involving compound interest using several worked examples. At the end of the article, you will be able to handle any arithmetic problem involving compound interest. Ensure to read to the end.
What Is Compound Interest?
Compound interest is the interest on a principal that is added to accumulated interests over time. In simple interest, the principal (the amount of money invested) remains the same year after year.
However, in compound interest, the interest you earned in the first year will be added to the initial principal invested. This now becomes the principal for the second year of investment. Unlike simple interest, your compound interest changes year after year even though the rate is the same.
Compound interest is usually used by commercial banks and big finance houses. Many loans that are given in these financial institutions are done with compound interest; therefore you need to have good knowledge of how to solve it.
General Formula For Compound Interest
The amount gotten at the end of successive investment years is given by:
A = P ( 1 + R/100)n
Where:
A = Amount
P = Principal
R = Rate
N = number of years
Now, in order to get our compound interest (C.I), we have to subtract the original principal from this amount
C.I = A – P
But A = P ( 1 + R/100)n
Therefore, C.I = P ( 1 + R/100)n – P
Worked Examples
Solving compound interest is pretty easy. You can calculate it like simple interest but you must bear in mind that the interest + original principal in the first year becomes the principal for the second year. We are going to explain these further using some worked examples.
Example 1
Find the compound interest on #900 for 3 years at 10% per annum.
Solution
C.I = P ( 1 + R/100)n – P
From the question above
P = 900
R = 10
n = 3
P ( 1 + R/100)n = 900(1 + 10/100)3
= 900 (110/100)3
900(1331/1000)
= 900 (1.331)
A = 1197.9
C.I = 1197.9 – 900
= #297.9
You can still solve this using an alternative method
P = 900
Recall that Simple interest = P x R x T/100
Interest in the Ist year = 900 x 10 x 1/100
= 90
Principal for second year= 900 + 90 = 990
Interest in the second year = 990 x 10 x 1/ 100
= 99
Principal in the third year = 990 + 99 = 1089
Interest for the third year = 1089 x 10 x 1/100
= 108.9
Amount after 3 years = 1089 + 108.9
= 1197.9
C.I = Amount – original P
= 1197.9 – 900
C.I = #297.9
So you can see that whichever way you use, you will still arrive at the correct answer.
Example 2
Find the C. I on a cassava farm investment of #20, 000 for 2 years at 10% per annum.
Solution
You will have to solve to get the amount first
A = P ( 1 + R/100)n
From the question, you are given the following:
P = 20, 000
R = 10
N = 2
A = 20,000 (1 + 10/100)2
= 20,000 (110/100)2
A = 20,000 (121/100)
= 20, 000 x 1.21 = 24, 200
C.I = A – P
= 24, 200 – 20, 000
C.I = #4,200
As a personal exercise, try to solve this second example using the alternative method. You will definitely arrive at the same answer if you follow the steps correctly.
This article has been able to show you how you can solve exercises on compound interest. You should endeavor to solve as many personal exercises as you can to gain mastery of the concept. If you have any questions or comments regarding this article, use the comment box below.
