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.
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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.
FAQs
Interest can be calculated in two ways: simple interest or compound interest. Simple interest is calculated on the principal, or original, amount of a loan. Compound interest is calculated on the principal amount and the accumulated interest of previous periods, and thus can be regarded as “interest on interest.”
What are the differences between simple interest compound interest and continuous compound interest? ›
Continuous compounding adds more interest, so it is better for investors, whereas discrete compounding adds less. However, all forms of compounding are better for investors than simple interest, which only calculates interest on the principal amount.
What is the difference between CI and SI concept? ›
The two ways are simple interest (SI) and compound interest (CI). Simple interest is basically the interest on a loan or investment. It is calculated on the principal amount. At the same time, Compound Interest is the interest calculated on interest.
What is the difference between simple interest and compound interest in simple terms? ›
Interest is the cost of borrowing money, expressed as a percentage of the total amount of the loan. Simple interest is an annual percentage of the amount borrowed, referred to as the annual interest rate. Compound interest is based on the sum of the principal amount and the previous interest payments on it.
Why is the difference between simple interest and compound interest critical? ›
Ultimately, the critical difference between compound and simple interest is whether or not the interest is added to the remaining principal owed and then accrues its own interest. Most credit and investment products—including savings accounts—will use compound interest.
What is the concept of simple interest? ›
What Is Simple Interest? Simple interest is an interest charge that borrowers pay lenders for a loan. It is calculated using the principal only and does not include compounding interest. Simple interest relates not just to certain loans. It's also the type of interest that banks pay customers on their savings accounts.
What is the key difference between simple interest and compound interest and how does this difference affect the effectiveness of each? ›
The difference between simple interest and compound interest is the way the interest accumulates. Simple interest accumulates only on the principal balance, while compound interest accrues to both the principal balance and the accumulated interest.
What are the basic concepts of SI and CI? ›
Simple interest is generally based on the principal amount of a loan or deposit whereas Compound Interest is based on the principal amount and also on the interest that accumulates on the principal every period. We have already discussed this in the SI vs CI definition.
What is CI vs SI interpretation? ›
CI, consecutive interpreting, refers to the mode in which the speaker and the interpreter take turns in speaking, while SI, simultaneous interpreting refers to the mode in which the interpreter uses a tranmitter to transmit the interpreted messages to receivers worn by the audience, when the speaker speaks ...
Is it SI or CI? ›
Simple interest (S.I.) is the sum paid back for using the borrowed money, over a fixed period of time whereas compound interest (C.I.)is calculated when the sum principal amount exceeds the due date for payment along with the rate of interest, for a period of time.
Key takeaways
- Most mortgages, student loans and auto loans charge simple interest.
- Simple interest typically results in lower total interest charged on a loan.
- Savings accounts typically compound the interest that someone earns.
- Compound interest generally leads to more total interest accumulated in a savings account.
What is the difference between how simple and compound interest are paid? Simple interest is paid on the principal only, compound interest is paid on both principal and interest.
What is the difference between compound and simple interest kids? ›
Simple interest is based on the amount of your deposit. Compound interest is based on the amount you deposit and the interest that accumulates in every period (monthly, quarterly, annually). Teach kids about investing today!
What is the difference between SI and CI formula? ›
The fundamental difference between simple interest and compound interest is that S.I. is calculated on the principal amount however C.I. calculation involves the principal amount + the interest that is collected on the principal amount every year.
Why choose compound interest over simple interest? ›
When it comes to investing, compound interest is better since it allows funds to grow at a faster rate than they would in an account with a simple interest rate. Compound interest comes into play when you're calculating the annual percentage yield. That's the annual rate of return or the annual cost of borrowing money.
Why is compound interest more powerful than simple? ›
This means, not only will you earn money on the principal amount in your account, but you will also earn interest on the accrued interest you've already earned. The idea of compound interest (as compared to simple interest) is fundamental to investing because it can ultimately lead to a greater return in your account.
What is the meaning of continuous compounding interest? ›
Continuously compounded interest is the mathematical limit of the general compound interest formula, with the interest compounded an infinitely many times each year. Or in other words, you are paid every possible time increment.
What is the key difference between simple interest and compound interest and how does this difference affect the effectiveness of each brainly? ›
Expert-Verified Answer
Simple interest is calculated solely on the principal amount, while compound interest takes into account both the principal and accumulated interest. Compound interest is more effective over time due to its exponential growth, making it a preferred choice for long-term investments or savings.
What is the difference between APR and APY? ›
APR represents the yearly rate charged for borrowing money. It includes fees but not including compounding. APY refers to how much interest you'll earn on savings and it takes compounding into account. The difference between APR and APY increases as interest is compounded more frequently.
