Simple Interest
Simple Interest is the interest paid on the principal amount for which the interest earned regularly is not added to the principal amount as we do in compound interest.
Let’s learn more about Simple Interest in detail, including its formula and examples.
Table of Content
Simple Interest Definition
Simple Interse is the method to calculate the interest where we only take the principal amount each time without changing it with respect to the interest earned in the previous cycle.
In simple terms, we can say that simple interest is the interest earned only because of the principal amount whereas compound interest is the interest earned on both principal and the previous interest earned.
Let us suppose we invest 100 rupees for 2 years at a rate of 10% for both simple interest and compound interest. Then for simple interest, the interest is calculated for 10% of 100 for the first year and similarly 10% of 100 for the second year.
Now for compound interest for the first year, the interest earned is the same 10% of 100 but for the second year, we take into account the interest earned in the previous year i.e. the interest earned in the second year is 10% of (100 + 10% of 100). Thus we see that generally for the same terms compound interest is greater than simple interest.
Simple Interest Formula
The formula to calculate Simple Interest is,
Where,Â
- P is the Principal amount,Â
- R is anuall Rate of Interest, andÂ
- T is the Time for which principal is invested.
Principal
The principal is the amount borrowed or invested. It is denoted by the letter “P”. The principal remains constant while calculating simple interest whereas in compound interest the principal increase after every cycle.
Rate
The rate of interest at which the principal amount is invested or borrowed for a specific period of time is called the rate.Â For Example, the rate of interest can be 5%, 10%, or 13%. Here the interest rate can be represented by “R”.
Time
The duration during which the principal is borrowed or invested is referred to as time. Â Time is symbolized by “T”.
Amount
When a person acquires a loan from a bank, he or she is required to repay the principal borrowed plus the interest amount and the total amount repaid is referred to as the Amount. It is denoted by the letter “A”.
Thus,
- A = P + SI
- P = A – SI
- A = P(1 + RT/100)
How to Find Simple Interest?
The simple interest on any sum of money is calculated using the steps discussed below,
Step 1: The Principal(P), Rate of interest(R) and time(T) of the loan amount is noted.
Step 2: Use Â the formula SI = (PÃ—RÃ—T/100) to calculate the Simple Interest
Step 3: Use all the values from Step 1 and substitute them in Step 2.
Step 4: Simplify the value obtained in Step 3 to get the required simple interest.
Let’s consider an example to understand the procedure better.
Example: Find the SI on rupees 10000 deposited for 3 years at 5% per annum.
Solution:
Given,
P = Rupees 10,000
R = 5% per annum
T = 3 yearsThus, SI = (PÃ—RÃ—T/100)
â‡’ SI = (10000Ã—5Ã—3)/100 = 1500
Thus the interest earn is rupees 1,500
Simple Interest and Compound Interest
Let’s understand the difference between simple interest and compound interest through the table given below:
Simple Interest vs. Compound Interest | |
---|---|
Simple Interest | Compound Interest |
Simple interest is calculated on the original principalÂ amount. | Compound interest is calculated on the accumulatedÂ sumÂ of principal and interest. |
Simple Interest can be calculated using the following formula:Â S.I.= P Ã— R Ã— T | Compound Interest can be calculated using the following formula:Â C.I.= P [(1 +R/100)^{T} – 1] |
Principle remains constant throughout the tenure. | Principle amount changes every year in the tenure. |
It is equal for every year on a certain principle. | It is different for every span of the time period as it isÂ calculated on the amount and not the principal. |
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Simple Interest Problems
Example 1: Rajesh takes a loan of Rs 20000 from a bank for a period of 1 year. The rate of interest is 10% per annum. Find the simple interest and the total amount he has to pay at the end of a year.
Solution:Â
Here,
Loan Sum = P = Rs 20000
Rate of Interest per year = R = 10%
Time (T) = 1 yearSI = (P Ã— R Ã—T) / 100Â
Â Â = (20000 Ã— 10 Ã—1) / 100Â
Â Â = Rs 2000Total Amount that Rajesh has to pay to the bank at the end of the yearÂ
Amount = Principal + Simple Interest
Â Â Â Â Â Â Â Â = 20000 + 2000Â
Â Â Â Â Â Â Â Â = Rs 22,000
Example 2: A person borrowed Rs 60,000 for 4 years at the rate of 2.5% per annum. Find the interest accumulated at the end of 4 years.
Solution:Â
Given,
Principal = Rs 60,000
Rate of Interest = 2.5 %
Time Â = 4 yearsSI = (P Ã— R Ã—T) / 100Â
Â Â = ( 60,000 Ã— 2.5 Ã— 4 ) / 100Â
Â Â = Rs 6000Â
Example 3: A person pays Rs 8000 as an amount on the sum of Rs 6000 that he had borrowed for 3 years. What will be the rate of interest?
Solution:
A = Rs 8000
P = Rs 6000Amount = Principal Â + Simple Interest
SI = A â€“ PÂ
Â Â = 8000 â€“ 6000Â
Â Â = Rs 2000Time (t) = 3 years
Rate (R) = ?SI = (P Ã— R Ã—T) / 100
R = (SI Ã—100) /(PÃ— T)
R = (2000 Ã— 100 /(6000 Ã— 3) Â
Â Â = 11.11 %Thus, the rate of interest R is 11.11 %.
FAQs on Simple Interest
What is Simple Interest?
The type of interest that is levied only on the principal amount and not on the aggregated interest amount is called simple interest. While calculating simple interest we do not add interest earned in the previous cycle to the amount in the next cycle.
What are Simple Interest formulas?
The formula to calculate the Simple Interest is,
SI = (PÃ—RÃ—T)/100
Where,Â
- P is the Principal amount,Â
- R is anuall Rate of Interest, andÂ
- T is the Time for which principal is invested.
What is Compound Interest Formula?
The formula to calculate the Compound Interest is,
C.I. = A – P
Where,
- A is the Amount i.e., A = P(1 + R/100)^{n }, andÂ
- P is the principal amount.
Are Home Loans Simple or Compound Interest?
Usually, all the loans given by financial institutions are compound interest. So home loans are generally of compound interest type.
What is the difference between Simple and Compound Interest?
The basic difference between Simple Interest and Compound Interest is that in simple interest the interest is paid only on the principal value, whereas, for compound interest, the interest is paid both on the principal value and the interest earned in previous intervals.
What Types of Loans Use Simple Interest?
Generally, all banks, financial institutions, and other money-lending companies apply compound interest on the loans as in this way they will earn will more interest from the customers. The calculations of compound interest are difficult and require a lot of calculation which is difficult for the common people to do.Â
So the loan disperses in the informal sector for a shorter period of time and is generally given on simple interest. For example, if a farmer wants to have a loan of 20,000 rupees for 3 months to prepare his crops he will go to a money lender who will give him the money at 3%-5% monthly interest. Here to make the calculations simpler these money lenders generally charge simple interest but at higher rates.