# Simple Interest

When you hear about simple interest, the word that may come to your mind is increase, something added or something extra gained. But is that what it really is? Let’s find out!

#### Create learning materials about Simple Interest with our free learning app!

• Flashcards, notes, mock-exams and more
• Everything you need to ace your exams

## What is Simple Interest?

Simple interest is a way of calculating the interest on an amount of money.

Simple interest is usually associated with borrowing or investing money. There are some terminologies you must get familiar with before we proceed. These terms are below.

1. Principal – Principal is the initial or original amount of money that was invested or borrowed. It is denoted by $P$.
2. Rate – Rate is the percentage change on the principal amount. It is denoted by $R$.
3. Time – Time is the period or duration in which the money is to be returned. It is denoted by $T$.
4. Amount – Amount is the sum of the principal and the simple interest. The amount is the total money you will get over a period of time. It is denoted by $A$.

Suppose you borrowed £200 from a friend and you both agreed that you’ll pay back the money after 6 months, at a rate of 1.5%. The principal amount is £200, the rate is 1.5% and the time is 6 months. The simple interest after 6 months will be the product of the principal, the rate, the time and the total amount will be the sum of the principal and the simple interest.

## Simple Interest formula

Calculating simple interest is done by finding the product of the principal amount, the rate, and the time. Hence, the formula for calculating simple interest is given by,

$SI=PRT$

where $SI$ is the simple interest,$P$ is the principal, $R$ is the rate and $T$ is the time.

In order to calculate the amount $A$, we add the principal to the simple interest and thus the formula for calculating the amount is given by

$Amount\left(A\right)=P+SI$.

There are other simple interest equations that can be derived from the simple interest formula. You might be asked to find just the principal amount, the rate, or the time when all other information is given.

In this case, you will have to substitute the values given in the formula and solve for the unknown. We can also derive a formula for the principal, the rate, and the time from the simple interest formula. Let’s see how.

We recall that the simple interest formula is

$SI=PRT$.

If we want to derive a formula for $P$, we will make $P$ the subject of the formula by dividing both sides by $RT$.

$\frac{SI}{RT}=\frac{PRT}{RT}\phantom{\rule{0ex}{0ex}}\frac{SI}{RT}=P$

Therefore, $P=\frac{SI}{RT}$

To get the formula for $R$, we will also follow the same procedure.

$SI=PRT$

Divide both sides by $PT$ to get,

$\frac{SI}{PT}=\frac{PRT}{PT}\phantom{\rule{0ex}{0ex}}\frac{SI}{PT}=R$

Therefore, $R=\frac{SI}{PT}$

To get the formula for $T$, we will proceed similarly.

$SI=PRT$

Divide both sides by $PR$ to get,

$\frac{SI}{PR}=\frac{PRT}{PR}\phantom{\rule{0ex}{0ex}}\frac{SI}{PR}=T$

Therefore, $T=\frac{SI}{PR}$

You don’t have to memorize all these formulas. You only need to remember the simple interest formula and you can always substitute your known values and solve to get the unknown.

The simple interest formula is sometimes written as,

$SI=\frac{PRT}{100}$

It is written like this because the rate $R$ is in percentage and in order to change from percentage to decimals, you have to divide by 100.

When you are solving a problem using the formula in this form, you only need to plug in the value for the rate directly but if you are using the other formula, you have to divide by 100 first.

## Steps for calculating simple interest

Below are the steps for calculating simple interest.

1. State the simple interest formula and identify the parameters given.
2. Input or substitute the given values into the formula.
3. Solve for the unknown.

## Simple Interest examples

Let's take some simple interest examples.

Find the simple interest on £5000 with a percentage increase of 5% over 4 years.

Solution

To find the simple interest, we will use the simple interest formula below.

$SI=PRT$

From the question, we have

$P=£5000\phantom{\rule{0ex}{0ex}}R=5%\phantom{\rule{0ex}{0ex}}T=4years\phantom{\rule{0ex}{0ex}}SI=?$

We will now substitute the values we have in the formula,

$SI=5000×\frac{5}{100}×4=£1000$.

This means that over 4 years, there will be an increase of £1000.

Calculate the simple interest earned after 2 years on £5000 at an interest rate of 5%.

Solution

Recall that the formula for calculating simple interest is

$SI=PRT$

Let’s list out the information given,

$T=2years\phantom{\rule{0ex}{0ex}}P=£5000\phantom{\rule{0ex}{0ex}}R=5%\phantom{\rule{0ex}{0ex}}SI=?$

Let’s substitute the values in the simple interest formula

$SI=5000×\frac{5}{100}×2=5000×0.05×2=£500$.

This means that the interest to be added to the principal after 2 years is £500.

We consider now examples where we are asked to find the rate, the principal or the amount.

If the simple interest on £300 over 2 years is £10, what is the rate?

Solution

Let’s first identify what we know and what we don’t know.

We know that

$P=£300\phantom{\rule{0ex}{0ex}}T=2YEARS\phantom{\rule{0ex}{0ex}}SI=£10\phantom{\rule{0ex}{0ex}}R=?$

We don’t know the rate $R$ of the principal amount at the end of 5 months.

Recall the simple interest formula

$SI=PRT$

We can just go ahead and use the formula for the rate derived earlier or we can directly substitute into the simple interest formula. Let's substitute directly.

$10=300×R×5\phantom{\rule{0ex}{0ex}}10=600R$

Divide both sides by 600 to get,

$\frac{10}{600}=\frac{600R}{600}\phantom{\rule{0ex}{0ex}}R=0.0167$

This is not our final answer because the rate we got is a decimal. The rate should be in percentage and to get it in percentage, we will have to multiply by 100.

$R=0.0167×100=1.67%$.

Find the principal invested if £170 of interest was earned in 2 years at an interest rate of 4%.

Solution

Let’s first list what we know and what are we looking for.

$P=?\phantom{\rule{0ex}{0ex}}SI=£170\phantom{\rule{0ex}{0ex}}T=2years\phantom{\rule{0ex}{0ex}}R=4%=\frac{4}{100}=0.04$

We are looking for the principal amount. We can substitute the values we have in the simple interest formula and solve for $P$ or we can use the formula for $P$derived earlier.

We will use the formula derived earlier.

$P=\frac{SI}{RT}=\frac{170}{2}×0.04=\frac{170}{0.08}=£2125$

Let's take another example of calculating the rate.

Find the rate if a principal of £8000 earned £3700 interest in 4 years.

Solution

As usual, we will list what we have. Stating what we have makes everything clearer.

$R=?\phantom{\rule{0ex}{0ex}}P=£8000\phantom{\rule{0ex}{0ex}}SI=£3700\phantom{\rule{0ex}{0ex}}T=4years$

Let us use the formula for the rate that was derived earlier.

$R=\frac{SI}{PT}=\frac{3700}{8000×4}=\frac{3700}{32000}=0.1156$

Remember that the rate is always in percentage. So, we have to convert to a percentage by multiplying by 100.

$R=0.1156×100\phantom{\rule{0ex}{0ex}}R=11.56%$

So the rate is 11.56%.

Find the amount and the simple interest earned on £550 over 3 years at an interest rate of 2%.

Solution

Let’s state what we know and what we are looking for.

$Amount\left(A\right)=?\phantom{\rule{0ex}{0ex}}SI=?\phantom{\rule{0ex}{0ex}}P=£550\phantom{\rule{0ex}{0ex}}T=3years\phantom{\rule{0ex}{0ex}}R=2%$

We are asked to find the amount and the simple interest. We have to find the simple interest first before we can find the amount.

$SI=PRT=550×\frac{2}{100}×3=£33$

The amount is the sum of the simple interest and the principal amount, thus

$Amount\left(A\right)=SI+P=33+550=£583$

## Difference between simple and compound interest

Just like simple interest, there is another type of interest called compound interest. The main difference between simple and compound interest is that with compound interest, the principal amount grows over time because interest is continuously added to it but with simple interest, the principal amount only grows once because interest is added just once. To find out more about compound interest, check out our article on Compound Interest.

## Simple Interest - Key takeaways

• Simple interest is a way of calculating the interest on an amount of money.
• The formula for simple interest is, $SI=PRT$ where $SI$ is the simple interest,$P$ is the principal, $R$ is the rate and $T$ is the time.
• Simple interest formula can also be written as $SI=\frac{PRT}{100}$. When you are solving a problem using the formula in this form, you only need to plug in the value for the rate directly but if you are using the other formula, you have to divide by 100 first.
• The amount is the sum of the principal and the simple interest, it is the total money you will get over a period. Its formula is given by $Amount\left(A\right)=P+SI$.
• The rate should always be in percentage.

#### Flashcards in Simple Interest 2

###### Learn with 2 Simple Interest flashcards in the free StudySmarter app

We have 14,000 flashcards about Dynamic Landscapes.

How do you solve a simple interest question?

A simple interest question is solved using the simple interest formula. The simple interest formula is:

S.I = P x R x T

where S.I is the simple interest

P is the principal amount

R is the rate

T is the time.

What is the formula for simple interest?

The formula for simple interest is:

S.I = P x R x T

where S.I is the simple interest

P is the principal amount

R is the rate

T is the time.

What is the difference between simple interest vs. compound interest?

The difference between simple and compound interest is that with compound interest, the principal amount grows over time because interest is continuously added to it but with simple interest, the principal amount only grows once because interest is added just once.

How to calculate simple interest and compound interest?

Simple interest and compound interest are calculated using their respective formulas.

StudySmarter is a globally recognized educational technology company, offering a holistic learning platform designed for students of all ages and educational levels. Our platform provides learning support for a wide range of subjects, including STEM, Social Sciences, and Languages and also helps students to successfully master various tests and exams worldwide, such as GCSE, A Level, SAT, ACT, Abitur, and more. We offer an extensive library of learning materials, including interactive flashcards, comprehensive textbook solutions, and detailed explanations. The cutting-edge technology and tools we provide help students create their own learning materials. StudySmarter’s content is not only expert-verified but also regularly updated to ensure accuracy and relevance.

##### StudySmarter Editorial Team

Team Math Teachers

• Checked by StudySmarter Editorial Team