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!

What is Simple Interest?

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 $RT$.

$$\begin{gathered} \frac{SI}{RT}=\frac{PRT}{RT} \\ \frac{SI}{RT}=P \end{gathered}$$

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,

$$\begin{gathered} \frac{SI}{PT}=\frac{PRT}{PT} \\ \frac{SI}{PT}=R \end{gathered}$$

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

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

Divide both sides by $PR$ to get,

$$\begin{gathered} \frac{SI}{PR}=\frac{PRT}{PR} \\ \frac{SI}{PR}=T \end{gathered}$$

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.

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.

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

Let's take another example of calculating the rate.

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.