# Simple Interest

In this chapter we’re going to be looking at simple interests. We shall explore how to calculate simple interest on loans, Interest rates, Time periods and Repayments. You must have some prior knowledge of working with percentages.

## What is an Interest

Money governs the world in some sense. We use money all the time through purchasing, selling and borrowing/lending. Many institutions such as banks make money by lending money and receiving profits when the loan is paid back. The extra money that the bank earns from the interest is what is known as interest. Examples of interests are; Simple interest, Compound interest, and Reducible interest.

In this chapter we shall be working with 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;

…which means after 3 years the simple interest will be;

### Example

Find the simple interest on a loan of £4200 borrowed for 5 years at an interest of 9.8% p.a.

Let’s find the first year interest first;

Now let’s multiply the first year interest by 5 to find the simple interest after 5 years.

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

If you observed carefully you might have noticed a pattern in our calculations. The formula we can conclude here is;

…where

**I** is the interest to find.

**P** is the amount borrowed.

**r** is the interest rate.

**n** is the years past.

Let’s use the formula with the example above.

Above we’ve 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. In this case we gave to adjust the n in the simple interest formula.

### Example

Find the simple interest on a loan of £6000 borrowed for 8 months at a rate of 11% p.a.

We know that the simple interest formula is;

And the months is 8/12 of a year which means;

The simple interest on a loan of £6000 borrowed for 8 months at a rate of 11% p.a. is £385.

## 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.

## Repayments

We can borrow money from the banks as loans. 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.

### Example

Joyce borrows £5000 from a bank. The bank charges 14% p.a. simple interest on the loan. Calculate her monthly repayment if she repays the loan in 3 years.

First we calculate the simple interest;

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

Now we divide this by the number of months in 3 years to find the monthly repayments.

Monthly repayment;

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

If you have been observing carefully you must have noticed a pattern from which we can form a formula to find the repayment. That is;