 # Difference Between CI and SI

Compound and simple interest questions are common in the exams. There are always 3-4 questions appearing from this topic. This topic is very vast and that is why we have decided to cover it in parts and today we are going to discuss the difference between simple interest and compound interest. ## Difference Between the Compound and Simple Interest

Sometimes you are given a situation and you have the option of repaying more it through compound interest or through simple interest. Obviously, you will choose simple interest because it is a cheaper option. Also, in compound interest, you are asked to pay the principal amount by levying interest on interest. But you would still need to determine the difference between the compound and simple interest. If the difference asked is for either two or three years than you can easily solve it through the formulas. Here are the formulas to the calculated difference in interests.

### Browse more Topics under Si And Ci If the difference between compound and simple interest is of two years than,
Difference = P(R)²/(100)²
Where P = principal amount, R = rate of interest

If the difference between compound and simple interest is of three years than,
Difference = 3 x P(R)²/(100)² + P (R/100)³.
Here also, P = principal amount, R = rate of interest

Test yourself by answering these 25 Practice Questions set of SI an CI.

### Solved Examples

Q. The difference between the compound and simple interest on a certain sum at 12% per annum for two years is Rs. 90. What will be the value of the amount at the end of 3 years if compounded annually?

Ans: Here, in this question, the difference is already given to us and we are required to find the principal amount. And using that principal amount we are required to find the amount compounded after three years. The difference is given for two years. So, the formula will be,

Difference = P(R)²/100²

Now, putting the values into the equation, we will find that,

90 = P(12)²/(100)²
90 x 100²/12² = P
P = Rs. 6250

Now, calculating the compound interest on Rs. 6250 will be,

A = 6250(1 + 12/100)³
A = 6250(112/100)³ => 6250(1.12)³ => Rs. 8780.80

So, the compounded amount after three years will be Rs. 8780.80

## Practice Questions

1. The ratio of interest between the compound and simple interest after two years on a sum of money to that after three years on the same sum, at the same rate of interest, is 11: 37. What will be the rate of interest?

A. 36.36 %            B. 34.24 %             C. 36.26 %             D. 38.96 %

2. What will be the difference between the simple interest on a principal of Rs? 500 is calculated at 5% per year for 3 years and 4% per year for 4 years?

A. Rs. 5                B. Rs. 40               C. Rs. 20                      D. Rs. 10

3. If it is given that simple interest is 10.5% annually and compound interest is 10% annually, what will be the difference between the interests on a sum of Rs? 2000 after 3 years?

A. Rs. 20              B. Rs. 30              C. Rs. 32                    D. Rs. 22