The Major Difference Between Simple Interest and Compound Interest is just that Simple Interest is calculated on the Principal whereas Compound Interest is calculated on the Principal Amount along with the Interest accumulated for a certain period of time. Both Simple and Compound Interest are widely used concepts in the majority of financial services. Check out Solved Example Problems for finding the difference between CI and SI in the later sections. Get to know about the concept Difference of Compound Interest and Simple Interest in detail by going through the entire article.
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How to find the Difference Between Simple Interest and Compound Interest?
Let us discuss in detail how to find the Difference between Simple Interest and Compound Interest. They are along the lines
Consider the Rate of Interest is the same for both Compound Interest and Simple Interest
Difference = Compound Interest for 2 years – Simple Interest for 2 Years
= P{(1+r/100)2-1} – P*r*2/100
= P*r/100*r/100
=((P*r/100)*r*1)/100
Solved Examples on Difference of Compound Interest and Simple Interest
1. Find the difference of the compound interest and simple interest on $ 10,000 at the same interest rate of 10 % per annum for 2 years?
Solution:
Simple Interest = PTR/100
= 10,000*10*2/100
= $2000
To find the Compound Interest firstly calculate the Amount
Amount A = P(1+R/100)n
A = 10,000(1+10/100)2
= 10,000(110/100)2
= 10,000(1.21)
= $12,100
Compound Interest = Amount – Principal
= 12,100 – 10,000
= $2,100
Difference between CI and SI = CI for 2 Years – SI for 2 Years
= $2100- $2000
= $100
2. What is the sum of money on which the difference between simple and compound interest in 2 years is $ 100 at the interest rate of 5% per annum?
Solution:
Simple Interest = PTR/100
Principal = P
T = 2 years
Substituting the given data in the formula for the simple interest we have
SI = (P*2*5)/100
To find the Compound Interest firstly, find out the Amount
Amount A = P(1+R/100)n
= P(1+5/100)2
CI = Amount – Principal
= P(1+5/100)2 – P
= P((1+5/100)2 -1)
Given the difference between CI and SI = $100
P((1+5/100)2 -1) – (P*2*5)/100 = $100
P((105/100)2 -1)-10P/100 = $100
P(1.1025-1)-10P/100 = $100
100P(0.1025)-10P =$10000
110.25P-10P = $10000
100.25P = $10000
P = $10000/100.25
= $99.75
Therefore, the Sum of Money is $99.75