Simple interest

When money is lent by a bank, whoever borrows the money normally makes a payment called interest for the use of the money.
The amount of interest paid depends on:

• the principal, which is the amount of money borrowed
• the rate (percentage) at which the interest is charged
• the time for which the money is borrowed.

In simple interest transactions, interest is paid on the original amount borrowed.

Example 3

I borrow $4000 from the bank for ten years at an interest rate of 7% per annum (‘per annum’ means ‘each year’ and is often shortened to p.a.).

What interest do I pay?

Solution

\begin{align}\text{Interest paid at the end of each year}&= 4000 × 7\%\\ &= 4000 × \dfrac{7}{100}\\ &= 4000 × 0.07\\ &= $280\\ \text{Total interest paid for 10 years}&= 280 × 10\\ &= $2800\end{align}

Formula for simple interest

We can develop a formula for simple interest. Suppose one borrows $P for T years at interest rate R. Using the same two-step process as above we can say:

\begin{align}\text{Interest paid at the end of each year} &= P × R\\ \text{Total interest paid over T years} &= P × R × T\\ &= PRT\end{align}

This gives us the well-known simple interest formula

\(I = PRT\) (interest = principal × rate × time)

Example 4

Find the simple interest on $8000 for 8 years at 9.5% per annum.

Solution

\begin{align}I &= PRT\\ &= 8000 × 9.5\% × 8\\ &= 8000 × 0.095 × 8\\ &= $6080\end{align}

The rate is given as a percentage. When you do the calculation, you need to write it as a decimal. This is an important skill for students to learn.

Some texts write the formula as:

\(I=\dfrac{PrT}{100}\)

So the above would be written:

\begin{align}I&=\dfrac{8000×9.5×8}{100}\\\\ &= $6080\end{align}