IB Maths AA 1.4 Notes

Simple interest

Financial mathematics applies sequences and series to money. In this topic, the main ideas are simple interest, compound interest and annual depreciation. These are part of the financial applications of geometric sequences and series, alongside calculating real value using inflation.

Simple interest is interest calculated only on the original amount invested or borrowed. If a principal of $P$ is invested at a rate of $r\%$ per year for $n$ years, then the interest added each year is constant. This means simple interest follows an arithmetic pattern.

The simple interest formula is

$A=P\left(1+\frac{rn}{100}\right)$

where $A$ is the final amount, $P$ is the original amount, $r$ is the annual interest rate and $n$ is the number of years.

A sum of $\$1000$ is invested at $6\%$ simple interest for $4$ years.

$A=1000\left(1+\frac{6\times4}{100}\right)$

$A=1000(1.24)$

$A=1240$

So the final amount is $\$1240$.