Interest: What is Interest, Types, Solved Examples
Saurav Sinha
| Updated: Apr 20, 2021 16:28 IST
Interest is the fee you pay when you borrow money, and it is a concept that dates back centuries. Surviving records show that interest was used in ancient Babylonian, Greek and Roman civilizations, and a moneylender is a key character in Shakespeare’s The Merchant of Venice. Two types of interest plans are commonly used today such as simple interest and compound interest. It is important to know how to calculate both.
In this article, we are going to cover the key concepts of Interest along with the various types of questions, and tips and tricks. We have also added a few solved examples, which candidates will find beneficial in their exam preparation. Read the article thoroughly to clear all the doubts regarding the same.
Also check Height and Distance concepts here once you are through with Interest concepts!
What is Interest?
Interest is the amount to be paid on the borrowed money or the amount received on the money lent. The borrowed money or the lent money is called Principal. The sum of the interest and the principal is called the Amount. The rate at which the interest is charged on the principal is called Rate of Interest. And finally, the period, for which the money is borrowed or deposited is called Time.
Types of Interest
Two types of interest plans are commonly used today such as simple interest and compound interest. Let us understand both of them from below.
(a) Simple Interest
Simple Interest is the product of the amount borrowed, the rate of interest and the amount of time for which the money is borrowed. When the interest is calculated only on the Principal for every year, it is called Simple Interest. Simple Interest can be calculated by the formula:
Simple Interest = (P x r x t) / 100, where, P = Principal, r = Rate of interest per year, t = Time period in years
(b) Compound Interest
Albert Einstein once said, “Compound interest is the eighth wonder of the world. He who knows it, earns it…..he who doesn’t, pays it”
It is the interest paid on the original principal amount and the accumulated past interest. Formulas related to compound Interest:
\(A=P(1+\frac{r}{100})^{t}\)
\(C.I=A-P\)
\(C.I=P[(1+\frac{r}{100})^{t} – 1]\)
Where, A = Amount, P = Principal, r = Rate of interest, t = Time period
The power of compounding is one of the greatest forces operating in the world of finance. With compounding, the value of money grows very quickly. A small number can grow into a large number in only a few steps.
Difference between Simple and Compound Interest
Simple interest is a one time charge for the use of the amount of money that is borrowed. Compound interest is a plan in which interest is computed on a schedule, usually consisting of an equal period of time, and is based on the balance of the outstanding loan.
The modern financial system is built on credit. While borrowing money from a bank to buy a car, to buy a house, or to finance an education are well known applications of using credit. Credit cards are another way for companies to make money as they charge compound interest.
It is rare that one can get a loan with simple interest from a commercial establishment. It is not unusual to get a loan with simple interest from a friend or relative to help with a down payment for a car or a house, provided that the lender chooses to be so generous.
When you’ve finished with Interest, you can read about Mensuration 2D concepts in depth here!
How to Solve Question-Based on Interest – Know all Tips and Tricks
Candidates can find different tips and tricks from below for solving the questions related to Interest.
Tip # 1: In Simple Interest, When the time period is given in months, we convert it into year by dividing it by 12 and when the time period is given in days, we convert it into year by dividing it by 365.
Tip # 2:In Compound Interest, When rate is compounded half yearly, then we take rate half and time double and when rate is compounded quarterly, then we take rate one fourth and time 4 times. If rate of compound interest differs from year to year, then
\(A=P(1+\frac{r_1}{100})(1+\frac{r_2}{100})(1+\frac{r_3}{100})…\)
Tip # 3: Tree Method – In this method we assume principle (on the basis of rate and time given) such that it eases our calculation part and at the last we compare it to the value given in question to get the required answer.
For example, If the 10% interest rate is given for 2 years then we will assume principle as Rs. 100 and if times is 3 years then we will assume principle as Rs. 1000. It is done to avoid any calculation in decimal form.
Tip # 4: Installment – When the sum of an amount is paid in parts, then each part of the amount paid is called installment.
For simple interest:
\(A=x+(x+\frac{x*r*1}{100})+(x+\frac{x*r*2}{100})+(x+\frac{x*r*3}{100}+…)\)
Where A = Total amount paid, x = Value of each installment, r = Rate of interest
For compound interest:
\(P=[\frac{x}{(1+\frac{r}{100})}+\frac{x}{(1+\frac{r}{100})^2}+\frac{x}{(1+\frac{r}{100})^3}…]\)
P = Loan amount, x = Value of each installment, r = Rate of interest
Interest Sample Questions
Question 1: Rs.1080 invested for 3 months gave an interest of Rs.27. The simple rate of interest per annum was?
Solution: 3 months = 3/12 years SI = (P × r × t)/100
⇒ 27 = (1080 × r × 3/12)/100
⇒ 27 = (90 × r × 3)/100
⇒ 27 = 270r/100
Hence, r = 10%.
Question 2: What will be the amount if a sum of Rs.25000 is placed at CI for 3 years while the rate of interest for the first, second, and third years is 4%, 8%, and 10%, respectively?
Solution: A = P (1 + r1/100)(1 + r2/100)(1 + r3/100) = 25000 (1 + 4/100) (1 + 8/100) (1 + 10/100) = 25000 (104/100) (108/100) (110/100) = 30888.
Question 3: Find compound interest for principal Rs 10000, time = 3 years and rate = 10%.
Solution:
Tree Method:
Step 1: Take principle (Rs 10000 here).
Step 2: For year at 10%, interest = Rs. 1000
For 2nd year, total interest = interest on principal + interest on interest of 1st year = 1000 + 100 = Rs. 1100
For 3rd year, total interest = interest on principal + interest on interest of 1st year + interest on interest of 2nd year = 1000 + 100 + 100 + 10 = Rs. 1210
Step 3: Add all interests = 1000 + 1100 + 1210 = Rs. 3310.
Question 4: Rs.9200 is invested at compound interest at the rate of 25% per annum for 2
Solution:
Effective Rate method:
Effective rate = x + y + xy/100 = 25 + 25 + (25 × 25)/100 = 56.25% Hence, C.I. = 9200 × 56.25% = Rs 5175
Question 5: What will be the difference between the compound interest and simple interest on Rs.3000 at 10% rate of interest for 2 years?
Solution: Difference between effective rate of compound interest and simple interest = 3.1%
Hence, Required difference = 1,00,000 × 3.1% = Rs. 3100
Question 6: The oven set is bought on 4 yearly installments at 10% simple interest. If equal instalments of Rs.2500 are made then find the amount to be paid as the price of the oven set.
Solution: Given rate = 10% and time = 4 years Let installment be Rs 100
Then, price = 1st payment + 2nd payment + 3rd payment + 4th payment = 100 + 110 + 120 + 130 = 460
Comparing with given installment, we get price, P = 2500 × 460/100 = Rs.11500
Question 7: A sum of Rs. P was borrowed and paid back in two equal yearly instalments, each of Rs. 35,280. If the rate of interest was 5% compounded annually, then the value of P is?
Solution: We know that,
\(P=[\frac{x}{(1+\frac{r}{100})}+\frac{x}{(1+\frac{r}{100})^2}+\frac{x}{(1+\frac{r}{100})^3}…]\)
Hence, P = [35,280/(1 + 5/100) + 35,280/(1 + 5/100)2] = [35,280 × (20/21)] + [35,280 × (20/21)²] = 33,600 + 32,000 = Rs 65,600
Also check Mixture and Alligations concepts here once you are through with Interest concepts!
Exams where Interest is Part of Syllabus
Questions based on interest come up often in various prestigious government exams some of them are as follows.
- SBI PO, SBI Clerk, IBPS PO, IBPS Clerk
- SSC CGL, SSC CHSL, SSC MTS
- LIC AAO, LIC ADO
- RRB NTPC, RRB ALP
- UPSC
- MPSC
- KPSC
- BPSC
- WBPSC
- Other State Level Recruitment Examinations
We hope you found this article regarding interest was informative and helpful, and please do not hesitate to contact us for any doubts or queries regarding the same. You can also download the Testbook App, which is absolutely free and start preparing for any government competitive examination by taking the mock tests before the examination to boost your preparation.
| If you are checking Interest article, also check the related maths articles in the table below: | |
| Sets | Comparision of Quantity |
| Rolles Theorem and Lagranges Mean Value Theorem | Speed Time and Distance |
| Mathematics | X Axis and Y Axis |
Interest FAQs
Q.1 What is Interest?
Ans.1 Interest is the amount to be paid on the borrowed money or the amount received on the money lent. More details can be found above.
Q.2 What is the difference between Simple Interest and Compound Interest?
Ans.2 Simple interest is a one time charge for the use of the amount of money that is borrowed. Compound interest is a plan in which interest is computed on a schedule, usually consisting of an equal period of time, and is based on the balance of the outstanding loan.
Q.3 How to solve the problem related to Interest?
Ans.3 Tips and tricks to solve the problems related to Interest are given above in the article. Kindly go through the article for the same.
Q.4 Where I will find some of the sample questions related to Interest?
Ans.4 Various example questions along with their solutions are given above in the article. Kindly go through the article for the same.
Q.5 In which exam questions from Interest come up?
Ans.5 Interest comes in various government competitive examinations on a regular basis. The names of such examinations are given above in the article.
