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https://courses.lumenlearning.com/wm-developmentalemporium/chapter/using-the-simple-interest-formula-to-calculate-interest-earned/

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Using the Simple Interest Formula to Calculate Interest Earned | Developmental Math Emporium

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Do you know that banks pay you to let them keep your money? The money you put in the bank is called the principal, P, and the bank pays you interest, I. The interest is computed as a certain percent of the principal; called the rate of interest, r. The rate of interest is usually expressed as a perc…

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https://www.math-only-math.com/word-problems-on-simple-interest.html

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Word Problems on Simple Interest are solved here:

1. Robert deposits $ 3000 in State Bank of India for 3 year which earn him an interest of 8%.What is the amount he gets after 1 year, 2 years and 3 years?

Solution:

In every $ 100, Robert gets $ 8.

(Since rate is 8% → 8 for every 100)

Therefore, for $ 1 he gets = $ 8/100

And for $ 2000 he gets = 3000 x 8/100

= $ 240

Simple Interest for 1 year = $ 240.

Simple Interest for 2 year = $ 240 x 2

= $ 480

Amount after 2 years = Principal (P) + Simple Interest (SI)

= 3000 + 480

= $ 3480

Amount after 3 years = Principal (P) + Simple Interest (SI)

= 3000 + 720 = $ 3720

We observe from the above example that, the Interest cannot be calculated without Principal, Rate and Time.

Therefore, we can conclude that Simple Interest (S.I.) depends upon:

And therefore, the formula for calculating the simple interest is

Simple Interest (SI) = {Principal (P) × Rate (R) × Time (T)}/100

Amount (A) = Principal (P) + Interest (I)

Principal (P) = Amount (A) - Interest (I)

Interest (I) = Amount (A) - Principal (P)

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Word Problems on Simple Interest | Formula for Calculating the Simple Interest

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Word Problems on Simple Interest are solved here: 1. Robert deposits $ 3000 in State Bank of India for 3 year which earn him an interest of 8%.What is the amount he gets after 1 year, 2 years and 3 years? Solution: In every $ 100, Robert gets $ 8.

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https://byjus.com/maths/simple-interest/

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Simple Interest is an easy method of calculating the interest for a loan/principal amount. Simple interest is a concept that is used in many sectors such as banking, finance, automobile, and so on. When you make a payment for a loan, first it goes to the monthly interest and the remaining goes towards the principal amount. In this article, let us discuss the definition, simple interest formula, and how to calculate the simple interest with examples.

What is Simple Interest?

Simple Interest (S.I) is the method of calculating the interest amount for some principal amount of money. Have you ever borrowed money from your siblings when your pocket money is exhausted? Or lent him maybe? What happens when you borrow money? You use that money for the purpose you had borrowed it in the first place. After that, you return the money whenever you get the next month's pocket money from your parents. This is how borrowing and lending work at home.

But in the real world, money is not free to borrow. You often have to borrow money from banks in the form of a loan. During payback, apart from the loan amount, you pay some more money that depends on the loan amount as well as the time for which you borrow. This is called simple interest. This term finds extensive usage in banking.

Simple Interest Formula

The formula for simple interest helps you find the interest amount if the principal amount, rate of interest and time periods are given.

Simple interest formula is given as:

\(\large \mathbf{SI=\frac{PTR}{100}}\)

Where SI = simple interest

P = principal

R = interest rate (in percentage)

T = time duration (in years)

In order to calculate the total amount, the following formula is used:
Amount (A) = Principal (P) + Interest (I)
Where,

Amount (A) is the total money paid back at the end of the time period for which it was borrowed.

The total amount formula in case of simple interest can also be written as:
A = P(1 + RT)
A = Total amount after the given time period

P = Principal amount or the initial loan amount

R = Rate of interest (per annum)

T = Time (in years)

Click here to get the simple interest calculator for quick computations.

Simple Interest Formula For Months

The formula to calculate the simple interest on a yearly basis has been given above. Now, let us see the formula to calculate the interest for months. Suppose P be the principal amount, R be the rate of interest per annum and n be the time (in months), then the formula can be written as:

Simple Interest for n months = (P × n × R)/ (12 ×100)

The list of formulas of simple interest for when the time period is given in years, months and days are tabulated below:

Difference Between Simple Interest and Compound Interest

There is another type of interest called compound interest. The major difference between simple and compound interest is that simple interest is based on the principal amount of a deposit or a loan whereas compound interest is based on the principal amount and interest that accumulates in every period of time. Let's see one simple example to understand the concept of simple interest.

Simple Interest Problems

Let us see some simple interest examples using the simple interest formula in maths.
Example 1: Rishav takes a loan of Rs 10000 from a bank for a period of 1 year. The rate of interest is 10% per annum. Find the interest and the amount he has to pay at the end of a year.
Solution:

Here, the loan sum = P = Rs 10000

Rate of interest per year = R = 10%

Time for which it is borrowed = T = 1 year

Thus, simple interest for a year, SI = (P × R ×T) / 100 = (10000 × 10 ×1) / 100 = Rs 1000

Amount that Rishav has to pay to the bank at the end of the year = Principal + Interest = 10000 + 1000 = Rs 11,000
Example 2: Namita borrowed Rs 50,000 for 3 years at the rate of 3.5% per annum. Find the interest accumulated at the end of 3 years. Solution:
P = Rs 50,000

R = 3.5%

T = 3 years

SI = (P × R ×T) / 100 = (50,000× 3.5 ×3) / 100 = Rs 5250
Example 3: Mohit pays Rs 9000 as an amount on the sum of Rs 7000 that he had borrowed for 2 years. Find the rate of interest. Solution:
A = Rs 9000

P = Rs 7000

SI = A - P = 9000 - 7000 = Rs 2000

T = 2 years

R = ?

SI = (P × R ×T) / 100

R = (SI × 100) /(P× T)

R = (2000 × 100 /7000 × 2) =14.29 %

Thus, R = 14.29%

Practice Questions

1. A sum fetched a total simple interest of Rs. 4016.25 at the rate of 9% per annum in 5 years. What is the sum?

2. A sum of Rs. 725 is lent at the beginning of a year at a specific rate of interest. After eight months, a sum of Rs. 362.50 more is lent but at the rate twice the former. At the end of the year, Rs. 33.50 is earned as interest from both loans. What was the actual rate of interest?

3. Simple interest on a certain sum is 16/25 of the sum. Find the rate of interest and time if both are numerically equal.

To learn more about other topics in Maths, visit BYJU'S - The Learning App.

Frequently Asked Questions on Simple Interest - FAQs

What is simple interest and example?

Simple Interest (S.I.) is the method of calculating the interest amount for a particular principal amount of money at some rate of interest. For example, when a person takes a loan of Rs. 5000, at a rate of 10 p.a. for two years, the person's interest for two years will be S.I. on the borrowed money.

What is simple interest and compound interest?

By definition, simple interest is the interest amount for a particular principal amount of money at some rate of interest. In contrast, compound interest is the interest calculated on the principal and the interest accumulated over the previous period.

What are the types of simple interest?

Simple interest can be considered as two categories when the time is considered in terms of days. They are ordinary and exact simple interests. Ordinary simple interest is a SI that takes only 360 days as the equivalent number of days in a year. On the other hand, exact simple interest is a SI that takes exact days in 365 for a normal year or 366 for a leap year.

What are the 2 types of interest?

In our daily lives, the two types of interest we generally deal with are simple interest and compound interest.

How do I calculate S.I.?

To calculate the SI for a certain amount of money (P), rate of interest (R) and time (T), the formula is:
SI = (PTR)/100
Here,
SI = Simple interest
P = Principal (sum of money borrowed)
R = Rate of interest p.a
T = Time (in years)

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Simple Interest (S.I) - Definition, Formula, and Example Problems

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Simple Interest is an easy method of calculating the interest for a loan/principal amount. Simple interest is a concept that is used in many sectors such as banking, finance, automobile, and so on. When you make a payment for a loan, first it goes to the monthly interest and the remaining goes towards the principal amount.

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https://www.cuemath.com/commercial-math/simple-interest/

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Simple interest is a method to calculate the amount of interest charged on a sum at a given rate and for a given period of time. In simple interest, the principal amount is always the same, unlike compound interest where we add the interest to the principal to find the principal for the new principal for the next year.

In this lesson, you will be introduced to the concept of borrowing money and the simple interest that is derived from borrowing. You will also be introduced to terms such as principal, amount, rate of interest, and time period. Through these terms, you can calculate simple interest using the simple interest formula.

What is Simple Interest?

Simple interest is a method of interest that always applies to the original principal amount, with the same rate of interest for every time cycle. When we invest our money in any bank, the bank provides us interest on our amount. The interest applied by the banks is of many types and one of them is simple interest.Now, before going deeper into the concept of simple interest, let's first understand what is the meaning of a loan.

A loan is an amount that a person borrows from a bank or a financial authority to fulfil their needs. Loan examples include home loans, car loans, education loans, and personal loans. A loan amount is required to be returned by the person to the authorities on time with an extra amount, which is usually the interest you pay on the loan.

Simple Interest Formula

Simple interest is calculated with the following formula: S.I. = (P × R × T)/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 R/100, thus 100 in the formula). To understand more about this formula, click here.

The principal is the amount that was initially borrowed (loan) from the bank or invested. The principal is denoted by P.

Rate is the rate of interest at which the principal amount is given to someone for a certain time, the rate of interest can be 5%, 10%, or 13%, etc. The rate of interest is denoted by R.

Time is the duration for which the principal amount is given to someone. Time is denoted by T.

The above formula can be further solved for any variable, P, R, or T. For example, by dividing both sides of the SI formula S.I. = (P × R × T)/100 by R × T, we get P = (100 × S.I.)/(R × T). Similarly, we can solve for either R or T.

Sometimes, the simple interest formula is written as just SI = PRT where R is the rate of interest as a decimal. i.e., if the rate of interest is 5% then R can be written as 5/100 = 0.05.

Amount: When a person takes a loan from a bank, he/she has to return the principal borrowed plus the interest amount, and this total returned is called the Amount.
Amount = Principal + Simple Interest
A = P + S.I.

A = P + PRT

A = P(1 + RT)

How to Find Simple Interest?

Simple interest is found by using the formula SI = (PRT)/100 where P is the principal, R is the rate of interest, and T is the duration. The values of P, R, and T have to be substituted in this formula to calculate the simple interest. Here is an example to understand the process better for same P and R values but for different T values.
Example:
Michael's father had borrowed $1,000 from the bank and the rate of interest was 5%. What would the simple interest be if the amount is borrowed for 1 year? Similarly, calculate the simple interest if the amount is borrowed for 2 years, 3 years, and 10 years? Also, calculate the amount that has to be returned in each of these cases.
Solution:
Principal Amount = $1,000, Rate of Interest = 5% = 5/100. (Add a sentence here describing the given information in the question.)

Now, we can also prepare a table for the above question adding the amount to be returned after the given time period.

What Types of Loans use Simple Interest?

Most banks these days apply compound interest on loans because in this way banks get more money as interest from their customers, but this method is more complex and hard to explain to the customers. On the other hand, calculations become easy when banks apply simple interest methods. Simple interest is much more useful when a customer wants a loan for a short period of time, for example, 1 month, 2 months, or 6 months.

When someone goes for a short-term loan using simple interest, the interest applies on a daily or weekly basis instead of a yearly basis. Consider that you borrowed $10,000 on simple interest at a 10% interest rate per year, so this 10% a year rate is divided into a rate per day which is equal to 10/365 = 0.027%. So you have to pay $2.73 a day extra on $10,000.

Simple Interest vs Compound Interest

Simple interest and compound interest are two ways to calculate interest on a loan amount. It is believed that compound interest is more difficult to calculate than simple interest because of some basic differences in both. Let's understand the difference between simple interest and compound interest through the table given below:

Simple interest is calculated on the original principal amount every time.

Compound interest is calculated on the accumulated sum of principal and interest.

It is calculated using the following formula: S.I.= P × R × T

It is calculated using the following formula: C.I.= P × (1 +R) T - P

It is equal for every year on a certain principal.

It is different for every span of the time period as it is calculated on the amount and not the principal.

Important Notes on Simple Interest:

If the rate of interest as a percentage is used then the SI formula is (PRT)/100. But if the rate of interest is used as a decimal (i.e., if we have already divided the rate by 100) then the SI formula is just PRT.

The rate of interest is the interest on every $100 for a fixed time period.

Interest is always more in the case of compound interest as compared to simple interest.

The formula or methods to calculate compound interest is derived from simple interest calculation methods.

Think Tank:

If the interest paid by Micheal is one-fifth of the total amount he has to pay after a certain time period, what is the time period if the rate of interest was 25%?

The interest on a sum lent at the rate of 10% per annum for a period of 20 months is equal to 1.5 times interest on $3,000 at the rate of 5% per annum in 3 years. What is the sum.

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Simple Interest Examples
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FAQs on Simple Interest

What is the Definition of Simple Interest?

Simple interest is a type of interest that is calculated only on the initial amount borrowed/invested, without considering any interest charged/earned in previous periods. It is a fixed percentage of the principal amount that is charged or earned over a specific period of time.

What is the Use of Simple Interest?

Simple interest is used in cases where the amount that is to be returned requires a short period of time. So, monthly amortization, mortgages, savings calculation, and education loans use simple interest.

What are Compound Interest and Simple Interest Formulas?

For a given principal P, time T, and rate of interest R%,

simple interest formula is PRT.

compound interest formula is P(1 + R)T - P.

What are the Types of Simple Interests?

Simple interest is of two types ordinary simple interest and exact simple interest. In ordinary simple interest, a year is considered of 365 days while calculating the interest while in exact simple interest, a year is considered 366 days if it is a leap year. Both methods use the same formula to calculate simple interest.

Are Home Loans Simple or Compound Interest?

Home loans take a long time to repay, so the interest added by the lender is usually compound interest.

Where to Find Simple Interest Calculator?

To find the simple interest calculator (SI calculator), click here. This calculator allows us to enter the values of principal, rate of interest, and time duration (in years/months/days) and finds the simple interest showing step-by-step solution.

Are Car Loans Simple or Compound Interest?

Car loans or auto loans use simple interest to calculate the interest. The borrower agrees to pay the money back, plus a flat percentage of the amount borrowed. But in case the borrower fails to repay the amount on time, the company or the lender may start charging compound interest.

What is the Difference between Simple and Compound Interest?

Simple interest is the interest paid only on the principal, whereas, compound interest is the interest paid on both principal and interest compounded in regular intervals.

How to Calculate Simple Interest?

Simple Interest is calculated using the following formula: SI = P × R × T, where P = Principal, R = Rate of Interest, and T = Time period. Here, the rate is given in percentage (r%) is written as r/100. And the principal is the sum of money that remains constant for every year in the case of simple interest.

How do I Calculate Simple Interest Monthly?

To calculate simple interest monthly, we have to divide the yearly interest calculated by 12. So, the formula for calculating monthly simple interest becomes (P × R × T) / (100 × 12).

What is Simple Interest Rate Formula?

Using the simple interest formula, SI = PRT/100. To find the rate R from this, we just solve this equation for R. Then we get R = (SI × 100) / (P × T).

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Simple Interest - Definition, Formula, Examples

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Simple interest is an interest that is calculated only on the principal amount for any given time period. The formula for simple interest is SI = (PRT)/100, where P is the interest, R is the rate, and T is the time period.

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Simple interest is interest being added to the original amount of money. To Calculate Simple Interest a formal was created which is: Principal (P) x Rate (R) x Time (T) all over 100.

Interest is like a fee someone pays for borrowing money from the owner.

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This Formula is Place over 100 Because The Variable For Rate Is A Percentage!

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Steps To Calculate Simple Interest and Amount

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Steps To Calculate Simple Interest and Amount

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Simple interest is applied in various calculations in banks and other financial institutions. It is not only used for certain loans but also to calculate the amount banks pay their customers