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
- Simple Interest
- Compound Interest with a Fractional Rate
- Data Sufficiency
- SI and CI Practice Questions
Learn more about Simple and Compound Interest in more detail here.
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
Learn more about the Quantitative Aptitude here.
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 %
The correct answer is A.
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
The correct answer is A.
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
The correct answer is C.
4. Raj decided to borrow a certain sum at the certain rate of interest from a bank which charges simple interest. He deposits the same sum at the same interest rate in another bank which offers compound interest. If the ratio of the difference of interests calculated by both the banks after 3 years to that after 2 years is 31/10, find the rate of interest.
A. 3.1 % B. 10 % C. 31 % D. 5 %
The correct answer is B.