# Simple Interest

## What is an Interest

Money is used everywhere. We use money all the time when purchasing, selling and borrowing/lending. Many institutions such as banks make money by lending money and receive profits when the loan is paid back. Or you may an extra money just or storing money in a bank.

If you put money into a bank or building society they will pay you interest on this money. This is a percentage of the original money in the account.

If you have borrowed money, from a bank or building society for a mortgage or other loan, you have to pay them interest.

Simple interest is calculated on a yearly basis (annually) and depends on the interest rate. The rate is often given per annum (p.a.) which means per year.

Examples of interests include; Simple interest, Compound interest, and Reducible interest. This article will be focusing on simple interest.

## Simple Interest Formula

Suppose John borrowed £1000 from HSBC bank for 3years and the bank charges simple interest at the rate of 10% p.a. That is 10% per year.

After 1 year the simple interest off the amount John borrowed will be; 10% of £1000 that is;

After 3 years the simple interest will be;

The simple interest formula is given by;

I ⇒ is the interest

P ⇒ is the original amount

r ⇒ is the interest rate

n ⇒ is the number of years

## Interest Rate, Principal, and Time

We can still use the simple formula to find out other values such as Interest rate, the principal, or the number of years past for a given simple interest. We find out these by rearranging the simple interest formula. The following is the simple interest formula.

We can rearrange this to find the interest rate as shown below;

We can find also rearrange it to find the time/years past.

## Simple interest examples

This section explores examples involving simple interest.

First find the first year interest and remember to convert the percentage into a decimal.

The simple interest on a loan of £4200 borrowed after 5 years is £1646.4.

The calculation we have just done is similar to using the simple interest formula. Simply multiply the percentage, original amount and number of years together.

I ⇒ is the interest

P ⇒ is the original amount

r ⇒ is the interest rate

n ⇒ is the number of years

## Simple interest over a fraction of a year

In the first example we calculated the simple interest in relation to full/whole years. In some cases you might have to find the simple interest for time periods which are not whole years. The simple interest formula can be adjusted to work in these cases.

If money is not left in a bank account for a whole year then only a fraction of the interest gets paid.

Interest for one year = 8.5% of £40

John will earn £1.70 in interest

First calculate the interest that John earns in one year. To find the interest work out;

Convert the percentage into a decimal first and work out 8.5% of 40.

6 months is half a year which means finding the 1 year interest and halving should provide the 6 months interest. Therefore…

Therefore the interest that John earns on 8.5% interest p.a., for 6 months is £1.70

The simple interest formula states that

There are 12 months in a year. This means that there are 8/12 months out of the entire year we have to work out in this question. Here we convert the number of years into a ratio of one year, i.e the number of years we have to work out is

Therefore the calculation that we have to work out is;

The simple interest on a loan of £6000 borrowed for 8 months at a rate of 11% p.a. is £440.

## Repayments

We can borrow money from the banks as aloan. We usually pay back this loan in small amounts over a certain period of time. These small amounts are known as repayments. We can make repayments weekly, monthly or yearly.

To calculate the amount of repayments we have to make over time we have to first calculate the total amount to be repaid.

This section explores examples and calculations involving repayments

First calculate the simple interest;

The amount to repay back after 3 years is the interest plus the amount borrowed

Therefore the monthly repayment is;

She will have to make a repayment of £197.22 per month.

You may have noticed that a formula can be formed here to make the repayments.

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