Simple Interest: Formula, Difference, Examples, Notes

Simple Interest (SI) is a fast and simple method to calculate the interest accrued for a loan. It is calculated by multiplying the daily interest rate with the principal and then with the number of days between payments. In SI, the principal amount always remains the same, unlike compound interest where we add the interest of previous years to the principal. SI is usually applied to small short term loans such as automobile loans, as well as some mortgages. In this article, we will introduce you to the concept of simple interest as well as principal, amount, rate of interest, and time period. Read on to learn more.

Simple Interest: Definition, Formula, Examples

When a borrower borrows some money from a lender, he (she) also promises to return it after a specified period. In addition to the principal amount, the borrower also pays some additional money as an interest to the lender. The extra sum is paid according to an agreement between the borrower and the lender. The agreement is generally in the form of rate per unit of the principal borrowed. It is usually given in the form of a per cent of the principal per annum. The interest of \(₹100\) for \(1\) year is known as the rate per cent per annum.

If interest is calculated uniformly on the original principal throughout the loan period, it is called simple interest.
If \(P =\) Principal, \(R =\) Rate of interest per annum and \(T =\) Time, then the SI formula is given by
\(S.I. = \frac{{P \times T \times R}}{{100}}\)

Amount: The total money paid back to the lender at the end of the specified period is called the amount.
That is, \(\rm{Amount} = \rm{Principal} + \rm{Interest}\)
or, \(A = P + I\), where \(‘A’\) stands for Amount, \(‘P’\) for Principal and \(‘I’\) for Interest.

Simple Interest Formula

Simple interest is computed using the formula: \(S.I. = \frac{{P \times T \times R}}{{100}}\) where \(P =\) Principal, \(R =\) Rate of Interest in \(\%\) per annum, and \(T =\) Time, usually calculated as the number of years. The rate of interest is in percentage \(r\%\) and is to be written as \(\frac{r}{100}\)

1. Principal: The principal is the amount that is initially borrowed from the bank. It is denoted by \(P\).
2. Rate: The rate of interest at which the sum is given to a borrower for a specified period. This rate is denoted by \(R\).
3. Time: Time is the period for which the sum is given to the borrower. Time is denoted by \(T\).
4. Amount: When an individual gets a loan from a bank, they have to return the principal borrowed plus the interest amount. This total returned is called the amount.

Simple and Compound Interests

Simple Interest: It is a technique to calculate the amount of interest charged on a sum at a given rate and for a given period. It is shortened as (S.I.). In SI, the sum is always the same, unlike compound interest, where we add the interest of earlier years principal to calculate that of the following year.
\(S.I. = \frac{{P \times T \times R}}{{100}}\)

Compound Interest: If the borrower and the lender agree to fix a specific interval of time (say, a year or a half year or a quarter of a year etc.) so that the amount \(( = \rm{Principal} + \rm{Interest})\) at the end of an interval becomes the principal for the following interval, then the total interest over all the intervals, computed in this way is called the compound interest and is abbreviated as \(C.I.\)
CI at the end of the specified period is equal to the difference between the amount at the end of the period and the original principal i.e.
\(C.I. = \rm{Amount} – \rm{Principal}\)
\(A = P{\left({1 – \frac{R}{{100}}} \right)^n}\)

Learn Important Simple Interest Formulas

Conversion Period: The fixed interval of time at the end of which the interest is calculated and added to the principal at the beginning of the interval is called the conversion period.
In other words, the period at which the interest is compounded is called the conversion period.

When the interest is calculated and added to the principal every six months, the conversion period is six months. Similarly, the conversion period is \(3\) months when the interest is calculated and added quarterly.

Note: If no conversion period is specified, the conversion period is taken to be one year.

Difference Between Simple and Compound Interests

Simple and compound interests are two methods to compute returns on a loan amount. It is thought that CI is more difficult to calculate than SI because of some fundamental differences in both. Understand the distinction between these two from the table given below:

Learn the Process of Calculation of Interest

Important Points to Remember about SI

1. An individual who borrows money is called the borrower.
2. An individual who lends money is called a lender.
3. The money borrowed from a lender referred to as the principal.
4. The extra money paid for by the borrower to the lender for having used his money is called the interest.
5. The total money paid back to the lender at the end of the specified period is called the amount.
6. Interest is thought to be simple unless it is calculated on the initial principal all over the loan period.
7. In computing the number of days, we will not count the day on which the money is accumulated, but the date of withdrawal is being counted.
8. Number of years \(= \frac{\rm{Number}\,\rm{of}\,\rm{days}}{365}\)

Solved Examples

Let us practice some questions on simple interest to understand the concept better.

Q.1. A sum of \(₹800\) is lent for one year at the rate of \(18\%\) per annum. Find the interest.
Ans: \(P =\) Principal \(=\,₹800\), \(R =\) Rate of Interest \(= 18\%\) per annum, \(T =\) Time \(= 1\) year
Let \(I\) be the interest. Then, \(I = \frac{{P \times R \times T}}{{100}}\)
\( \Rightarrow I = \frac{{800 \times 18 \times 1}}{{100}} = 8 \times 18 = ₹144\)
Hence, the interest is \(₹144\).

Q.2. Find the compound interest on \(₹12000\) for \(3\) years at \(10\%\) per annum compounded annually.
Ans: We know that the amount \(A\) at the end of \(n\) years at the rate of \(R\%\) per annum when the interest is compounded annually is given by \(A = P{\left({1 + \frac{R}{{100}}} \right)^n}\)
Here, \(P = ₹12000\), \(R = 10\%\) per annum and \(n = 3\)
\(∴\) Amount \(A\) after \(3\) years \( = P{\left({1 + \frac{R}{{100}}} \right)^3}\)
\( = 12000{\left({1 + \frac{{10}}{{100}}} \right)^3}\)
\( = 12000{\left({1 + \frac{{1}}{{10}}} \right)^3}\)
\( = 12000{\left({\frac{{11}}{{10}}} \right)^3}\)
\( = 12000 \times \frac{{11}}{{10}} \times \frac{{11}}{{10}} \times \frac{{11}}{{10}} = ₹15972\)
Amount \(= ₹15972\)
CI \(= \rm{Amount} – \rm{Principal}\)
CI \(= ₹15972 – ₹12000 = ₹3972\)
Hence, the compound interest is \(₹3972\).

Q.3. Find the interest on \(₹1200\) at \(6\%\) per annum for \(146\) days.
Ans: \(P = ₹1200\), \(R = 6\%\) per annum, \(T = 146\) days \(=\frac{146}{365}\) year \(=\frac{2}{5}\) year.
\(I = \frac{{P \times R \times T}}{{100}}\)
\(I = ₹\left({\frac{{1200 \times 6 \times \frac{2}{5}}}{{100}}} \right) = ₹\left({\frac{{144}}{5}} \right) = ₹28.80\)
Hence, the interest is \(₹28.80\)

Q.4. What principal will amount \(₹900\) in \(6\) years at \(10\%\) SI?
Ans: We have, \(A = ₹900\), \(T = 6\) years, \(R = 10\%\) per annum,
Let \(P\) be the principal and \(I\) be the interest.
Then, \(I = \frac{{P \times R \times T}}{{100}}\)
\( \Rightarrow I = \frac{{P \times 10 \times 6}}{{100}} = ₹\frac{{3P}}{5}\)
Now, \(A = P + I\)
\(\Rightarrow 900 = P + \frac{3P}{5}\)
\(\Rightarrow 900 = \frac{5P + 3P}{5}\)
\(\Rightarrow 900 = \frac{8P}{5}\)
\(\Rightarrow P = \frac{900 \times 5}{8} = 562.50\)
Hence, principal \(= ₹562.50\)

Q.5. In how many years will \(₹750\) amount to \(₹900\) at \(4\%\) per annum?
Ans: Here, \(P = ₹750\), \(A = ₹900\), \(R = 4\%\) per annum.
Let \(₹750\) amount to \(₹900\) at \(4\%\) per annum in \(T\) years.
Now, Interest \(= \rm{Amount} – \rm{Principal}\)
\(= ₹900 – ₹750 = ₹150\)
\(I = \frac{{P \times R \times T}}{{100}}\)
\( \Rightarrow 150 = \frac{{750 \times 4 \times T}}{{100}}\)
\( \Rightarrow T = \frac{{150 \times 100}}{{750 \times 4}} = 5\) years
Thus, \(₹750\) amounts to \(₹900\) at \(4\%\) per annum in \(5\) years.

Summary

In this article, we learnt about simple interest, its definition, formula, difference from compound interest, important points, solved examples. This article’s learning outcome is to make students learn that SI is more advantageous for borrowers than CI, as it keeps overall payments lower.

Learn All the Concepts on Compound Interest

Frequently Asked Questions (FAQs)

The most frequently asked questions on the topic are answered here:

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