# Interest

Most times when you borrow money from someone or loan money to someone, the money paid back is more than the money that was taken, and, sometimes, the extra money may increase over time. The extra money made is called interest

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As we continue, we will understand better what this means in maths.

## Interest meaning

Interest is a fee paid on borrowed money or on a loan.

The term used to describe the borrowed money or the loan is called the principal amount. If you borrow money from someone or loan to someone, the charges on the principal amount are called the interest rate.

The interest rate is expressed in percentages.

Imagine a scenario where you borrow £500 from a friend and the friend says to pay it back in two months with an interest rate of 2%. This means that in two months, you will pay back £500 plus 2% of £500 which is £510. The interest is £10.

Imagine another scenario where you keep your money in a savings account. Keeping your money in a savings account means that you are loaning your money to the bank for use. In return, the bank pays you back with interest at the end of each year. The longer you keep your money in the account, the more interest you will receive.

## Interest formula

There are two types of interest:

We are going to explore in the following, the types of interest and their corresponding formulas.

## Simple interest in math

Simple Interest is used to find the interest on a principal amount. To find the simple interest, you will need to know the principal amount, the interest rate, and the time in which the money is to be paid back or returned.

### Simple interest formula

To calculate simple interest we will use the simple interest formula below.

$SI=PRT$

where $SI$ is the simple interest

$P$ is the principal amount

$R$ is the rate (interest rate)

$T$ is the time interval.

Sometimes when dealing with questions on simple interest, you may be asked to find the amount that is to be paid back. This is different from finding simple interest. The amount that should be paid back is the sum of the principal amount and the simple interest. The formula is therefore

$Amount=P+SI$

## Compound interest in math

Compound Interest refers to the amount of interest that has been gathered or earned over time on an amount of money. This is mostly used in banks.

When you put money in a savings account and you leave it there for a long time, you find out that each year your money is increased with a particular interest rate. The interest will continue to be added over time provided the money stays in the bank. This interest gathered over time is what is called compound interest.

Compound interest is also described as interest on interest because new interest is always added. With questions relating to compound interest, you are looking for the amount of money that is gained with the compound interest over a time interval.

### Compound interest formula

There is a formula used for compound interest. The compound interest formula is below.

$Amountafternyears=Principal×{\left(1+rate\right)}^{n}$

where $n$ is the Number of years.

## Interest examples

We have seen what simple and compound interest are and the formula used to calculate them. Let's now see how to use these formulas in the examples below.

### Simple interest examples

Let’s take some simple interest examples.

Hannah borrowed £600 from her friend for a year at an interest rate of 5%. What is the simple interest?

Solution

The information given is

$P=£600\phantom{\rule{0ex}{0ex}}T=1year\phantom{\rule{0ex}{0ex}}R=5%\phantom{\rule{0ex}{0ex}}SI=?$

The simple interest can be calculated via the formula,

$SI=PRT\phantom{\rule{0ex}{0ex}}=600×\frac{5}{100}×1\phantom{\rule{0ex}{0ex}}=600×0.05\phantom{\rule{0ex}{0ex}}=£30$

Let's take another interest example.

I borrowed £20,000 from the bank for three years at an interest rate of 10% per annum. How much will I pay back at the end of the three years?

Per annum means per year

Solution

The first thing we need to do is list out all information given to us.

$P=£20000\phantom{\rule{0ex}{0ex}}T=3years\phantom{\rule{0ex}{0ex}}R=10%\phantom{\rule{0ex}{0ex}}Amounttobepaidback=?$

The formula to find the amount is given by

$Amount=P+SI$

To find the amount, we must first calculate the simple interest using the simple interest formula, which is,

$SI=PRT\phantom{\rule{0ex}{0ex}}=20000×\frac{10}{100}×3\phantom{\rule{0ex}{0ex}}=20000×0.1×3\phantom{\rule{0ex}{0ex}}=£6000$

We will now find the amount which is the sum of the principal and the simple interest.

$Amount=20000+6000\phantom{\rule{0ex}{0ex}}=£26000$

#### Simple interest principal amount examples

There are questions concerning simple interest where you will be asked to find the principal amount or the rate. What you will do in this situation is to substitute the values given in the simple interest formula and find the unknown.

Let’s see an example.

The simple interest on an amount of money is £1000. The Percentage interest rate is 4% and it is to be paid after four years. What is the principal amount?

Solution

In the question, we are given the simple interest, the interest rate, and the time.

$SI=£1000\phantom{\rule{0ex}{0ex}}R=4%\phantom{\rule{0ex}{0ex}}T=4years\phantom{\rule{0ex}{0ex}}P=?$

The simple interest formula is given by

$SI=PRT$

We substitute the values we have in the simple interest formula,

$1000=P×\frac{4}{100}×41000\phantom{\rule{0ex}{0ex}}=P×0.04×41000\phantom{\rule{0ex}{0ex}}=0.16P$

We need to isolate P and make it the subject of the formula so we can find its value by dividing both sides of the equation by 0.16. We get:

$\frac{1000}{0.16}=\frac{0.16P}{0.16}\phantom{\rule{0ex}{0ex}}P=\frac{1000}{0.16}\phantom{\rule{0ex}{0ex}}P=£6250$

The approach used in the example above is used when you are asked to find something other than simple interest.

### Compound interest examples

Let’s take some compound interest examples.

Someone deposited £10,000 to his savings account to earn an interest of 10% every year for five years. How much will be withdrawn at the end of the fifth year?

Solution

The information given in the question is below.

$P=£10000\phantom{\rule{0ex}{0ex}}R=10%\phantom{\rule{0ex}{0ex}}n=5years\phantom{\rule{0ex}{0ex}}Amountafter5years=?$

The compound interest formula is:

$Amountafternyears=Principal×{\left(1+rate\right)}^{n}\phantom{\rule{0ex}{0ex}}=10000×{\left[1+\frac{10}{100}\right]}^{5}\phantom{\rule{0ex}{0ex}}=10000×{\left[1.1\right]}^{5}\phantom{\rule{0ex}{0ex}}=10000×1.61051\phantom{\rule{0ex}{0ex}}=£16105.1$

£16 105.1 is the amount the person will have after five years because of the compound interest.

#### Compound interest principal amount examples

Just like for the simple interest, you may come across questions where you may be asked to find the principal amount. What you will do in this situation is to substitute the values you have and solve for the unknown.

Let’s see the example below.

If you are to get £20,000 after five years at an interest rate of 10%, what is the principal amount you invested?

Solution

The information given in the question is below.

$Amountafter5years=£20000\phantom{\rule{0ex}{0ex}}Rate=10%\phantom{\rule{0ex}{0ex}}n=5years\phantom{\rule{0ex}{0ex}}Principal=?$

The compound interest formula is,

$Amountafternyears=Principal×{\left(1+rate\right)}^{n}$

What we are going to do is substitute the known values and solve for the unknown.

$20000=P×{\left(1+\frac{10}{100}\right)}^{5}20000\phantom{\rule{0ex}{0ex}}=P×{\left(1+0.1\right)}^{5}20000\phantom{\rule{0ex}{0ex}}=P×{1.1}^{5}20000\phantom{\rule{0ex}{0ex}}=1.61P$

We have to make P the subject of the formula and to do that, we will divide both sides of the equation by 1.61.

$\frac{20000}{1.61}=\frac{1.61P}{1.61}\phantom{\rule{0ex}{0ex}}P=\frac{20000}{1.61}\phantom{\rule{0ex}{0ex}}P=£12422.36$

To get in-depth knowledge on simple and compound interest, check out our Simple Interest and Compound Interest articles.

## Interest - Key takeaways

• Interest is a fee paid on borrowed money or on a loan.
• The types of interest are Simple interest and Compound interest.
• Simple interest is calculated by finding the product of the principal amount, rate, and time.
• Simple interest is used to find the interest on a principal amount.
• Compound interest refers to the amount of interest that has been gathered or earned over time on an amount of money.

#### Flashcards in Interest 14

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What is the math formula for interest?

The formula for interest depends on the type of interest that is to be calculated. If it is a simple interest, the formula used is:

S.I = PRT

where S.I is the simple interest

P is the principal amount

R is the rate (interest rate)

T is the time interval

If it is compound interest, the formula is,

Amount after n years = Principal x ( 1 + rate)^n

What is interest in Math?

Interest is a fee paid on borrowed money or on a loan.

What are simple and compound interests?

Simple interest is used to find the interest on a principal amount.

Compound interest refers to the amount of interest that has been gathered or earned over time on an amount of money.

How do you calculate interest in maths?

How to calculate interest in maths: formulas are used depending on the type of interest. If it is simple interest, the formula will be:

Simple Interest = Principal x Rate x Time

If it is compound interest, the formula will be:

Amount after years = Principal x (1 + rate)^n

What are three different methods of calculating interest?

Three methods for calculating interest are:

1.  Simple interest
2. Compound interest
3. Continuous compound interest

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