Difference of Compound Interest and Simple Interest | How to Calculate Difference Between SI and CI?

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.

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