Content Writer-SME | Updated On - Nov 19, 2024
In the simple interest formula, the amount lent is the principal amount (P), the time for which the amount lent is the time period (T) and the rate at which the money is lent is known as the rate of interest (R).
Interest is the income of money lenders over the money they lend to people. In economics, money is said to have time value, which means that the value of money increases with time. This makes the worth of money increase when repaid after a period of time.
Simple Interest
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Simple interest formula refers to a formula that helps us to calculate the interest payable for a certain amount borrowed/ lent for a period of time. Interest is simply the income that financial organisations like a bank, money lenders, etc. Earn by lending money to common people and business houses.
Interests are basically of two types: simple interest and compound interest. Simple interest is the simplest form of interest where the interest is calculated on the same principal amount till the end of the time period for which the money was lent. However, the compound interest will have an increasing principal amount and thus increasing interest payable. This makes simple interest an acceptable form of interest calculation.
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Simple Interest Formula
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Simple interest refers to the calculation of interest accrued for a certain amount over a period of time, without any change in the amount lent. In mathematics, the simple interest formula is given by:
Simple Interest = (principal x Time period x Rate of Interest) /100
Or
\(S.I =\frac {P\times R \times T}{100}\)
In the above formula, the principal amount (P) would be the amount borrowed. The amount borrowed becomes the base for payment of interest. The more the amount borrowed, the more will be the interest payable. Rather than in the Compound interest formula, the principal amount will remain the same till the borrowed amount will be repaid.
The time period (T) will be the period for which the amount would be borrowed. This could be days, months, or even years. For example, if Mr. A borrowed Rs.10,000 from a money lender and agreed to pay back the money after 3 months, then 3 months would be the time period.
The rate of interest (R) is the rate for which the money is borrowed/lens. The more the interest rate would be, the more would be the interest payable on the same principal amount. For example, when a person borrows Rs. 1,00,000 at an interest rate of 10%, he would have to pay Rs. 10,000 as interest. Whereas, if the rate of interest was 15%, he would have to pay Rs.15,000 as interest for the same Rs.1,00,000
The sum of both the principal amount and the interest found using the formula is called the amount payable. The amount payable is what we ought to return to the person from whom we borrowed the amount.
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Applications of simple interest
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Being simple to calculate and easy to understand, most money lenders use simple interest formulas to calculate interest for money they lend. Following are some of the real-life applications of the simple interest formula.
- In banks, for providing short-period lending like commercial deposits.
- In NBFCs for charging over mortgages for which they provide funds to the mortgagor.
- In other financial institutions led by unrecognised money lenders, a simple interest formula is easy to calculate.
- By companies while providing financial assistance to buy products.
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Things to remember
- Simple interest and compound interest are two major types of interest out of which, simple interest is the easiest and most popular one.
- Simple interest is calculated using the simple interest formula,
Simple Interest = (principal x time period x rate of interest) /100
- The principal amount remains constant in the simple interest calculation, which makes the interest calculation easy and reduces the interest burden of the borrower.
- Simple interest formula is very commonly used in the calculation of interest for a consumer loan, mortgage interest, EMIs, etc.
Sample Questions
Ques. Why does simple interest have wide popularity in usage? (3 marks)
Ans. Simple interest formula has wide application in the field of banks, finance companies, loan providers, etc... This wide popularity of simple interest is due to the following reasons:
- Ease of application of simple interest formula.
- Anyone can easily remember simple interest formulas.
- The amount payable (principal amount + interest amount) is less for customers when compared to the compound interest formula.
Ques. What is the factor that makes simple interest different from compound interest? (2 marks)
Ans. The major difference of the simple interest formula from that of a compounded interest formula is that in the simple interest formula the principal amount and interest amount remains stable whereas, in compound interest, both the principal amount and interest amount keep on changing over the period of time.
Ques. From the formula to calculate simple interest, derive a formula to calculate the principal amount. (3 marks)
Ans.
Simple Interest = (principal x time period x rate of interest) /100
OR
SI = P.T.R/100
To derive a formula to calculate Principal Amount, we should keep Principal Amount (P) alone on the right-hand side, and take all other factors (i.e. time period (T) x Rate of interest (R)/100) to the left-hand side, step-by-step.
SI = P.T.R /100
→ SI x 100 = P.T.R
→ SI x 100 / (T.R) = P
OR
P = SI x 100/ (T.R)
OR
Principal Amount = simple interest x 100 / (time period x rate of interest)
Ques. State some real-life situations where the simple interest formula becomes applicable. (3 marks)
Ans. The simple interest formula has much application in real life when compared to the compound interest formula. This is mainly due to two reasons:
- Simple interest formula is easy to remember and calculate.
- Simple interest formula gives less inert burden over the customers.
For these reasons, simple interest formula is widely applied in the following areas:
- In banks, for providing short-period loans.
- In NBFCs for charging over mortgages.
- In other financial institutions led by unrecognised money lenders.
Ques. Sreeram was confused when he was asked to calculate the rate of interest when the interest amount of three months and the principal amount were given. Can you help him? (hint: make use of the formula of simple interest) (3 marks)
Ans.
Simple Interest = (principal x time period x rate of interest) /100
OR
SI = P.T.R/100
To derive a formula to calculate the rate of interest, we should keep the rate of interest (R) alone on the right-hand side, and take all other factors (i.e. principal Amount (P) x time period (T) /100) to the left-hand side, step-by-step.
SI = P.T.R /100
→ SI x 100 = P.T.R
→ SI x 100 / (P.T) = R
OR
R = SI x 100/ (P.T)
OR
Rate of interest = simple interest x 100 / (Principal Amount x time period)
In the above situation, Sreeram can replace the Time period (T) with 3 to answer the question he was asked.
Ques. Sachin lends Rs. 10,000 from Dhoni, on 31st March 2016 and promised to repay him on 31st March 2017. Dhoni agreed to him but asked Sachin to repay Rs.11, 200, instead. Explain to Sachin why Dhoni asked for Rs.11, 200. (4 marks)
Ans.
Here, the amount Sachin lent from Dhoni was Rs. 10,000. Therefore, the Principal amount (P) = 10,000.
Also, Sachin promised to repay the amount on 31st march 2017 that is after exactly one year. Therefore, the time period (T) = 1
The amount payable by Sachin is Rs.11,200.,
Amount payable = Principal amount + simple interest
→ 11,200 = 10,000 + simple interest
→ Simple interest = 11,200 – 10,000
= 1,200
Simple Interest = (principal x time period x rate of interest) /100
Restructuring the above formula to find rate of interest, we will get,
Rate of interest = simple interest x 100 / (Principal Amount x time period)
→ Rate of Interest = 1,200 x 100 / (10,000 x 1)
[Where, principal amount = 10,000 and time period = 1]
Therefore, Rate of Interest = 12%
Now, we know that Dhoni demanded Rs.11,200 instead of Rs.10,000, considering the interest he should get at a 12% rate of interest.
Ques. When Mr. A borrowed money from Mr. B, Mr. A was asked to pay Rs.2000 per month for a year. If the amount Mr. A borrowed was Rs.1,00,000, calculate the rate of interest at which the money was lent. (3 marks)
Ans.
Rate of interest = simple interest x 100 / (Principal Amount x time period)
Here,
Simple interest = 2,000
Principal amount = 1, 00,000
Time period = 12
Applying the above information to the formula, we will get
Rate of interest = 2,000 x 100 / (1,00,000 x 12)
= 2,00,000/ 12,00,000
= 0.16667
Therefore, rate of interest = 16.67 %
Ques. Rahul borrowed Rs. 2,54,648 from Muthoot Fincorp.ltd., pledging his motor car. He was offered an option to borrow for a 12.35% interest rate for 3 months and a 13.45% rate for 12 months. If he chooses the second option, what will be the total amount payable by him? (4 marks)
Ans.
When considering the second option we have the following information from the question:
Principal amount = 2,54,648
Rate of Interest = 13. 45 %
Time period = 12 months
Also,
Simple Interest = (principal x time period x rate of interest) /100
Applying the available information to the formula we will get,
Simple interest = ( 2,54,648 x 12 x 13.45 )/100
= 4,11,002 (approximately)
Therefore,
The total amount payable = principal amount + simple interest
= 2,54,648 + 4,11,002
= 6,65,650
Ques. Priya borrowed a certain amount from Rahul enterprise at an interest rate of 12% for three months. If Priya paid back Rs. 12,360 after 3 months, how much did she borrow from him? (4 marks)
Ans.
Here, the following information is provided:
Rate of interest = 12 %
Time period = 3
Amount payable = 12,360
Amount payable = principal amount + simple interest
→ 12,360 = principal amount + simple interest
Let the principal amount be ‘X’,
Then, Simple Interest = (principal x time period x rate of interest) /100
→ Simple interest =(X x 12 x 3)/ 100
Then,
12,360 = X + (0.36 X )
→ 12,360 = 1.36 X
Therefore,
X = principal = 12,360/1.36
= 9,0882
Therefore, the amount borrowed = Rs. 9,0882.
Ques. Calculate simple interest of Rs. 45,000 at interest rate 25% per annum for 45 days. (3 marks)
Ans. Simple Interest = (principal x time period x rate of interest) /100
Here, principal amount = 45,000
Rate of interest = 25%
Time period = 45/365
= 0.123
[Note that the rate of interest is given for a year. so the time period is converted to year i.e., 45 days means 0.123 years]
Therefore, simple interest = (45,000 x 25 x 0.123) /100
= 1384 (approx.)
Therefore, simple interest = 1384
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