Compound interest
Compound interest is similar to simple interest in that the interest is added on annually.
The difference between the two is that simple interest is a fixed amount of interest that is added on every year, whereas with compound interest the amount you are calculating interest on, changes every year.
The interest is calculated for the first year and is then added on to the original amount to give you the amount after the first year.
The interest for the second year is then calculated from the amount after the first year, which then gives you a different amount of interest gained from the first year.
Example
Calculate the amount of compound interest Jane will have earned on \(\pounds6000\) at \(2.8\%\) for 3 years.
Method 1
Year 1
\(2.8\% \,of\,6000\)
\(= 0.028 \times 6000\)
\(= \pounds168\)
Year 2
\(2.8\% \,of\,6168\)
\(= 0.028 \times 6168\)
\(= \pounds172.70\)
Year 3
\(2.8\% \,of\,6340.70\)
\(= 0.028 \times 6340.70\)
\(= \pounds177.54\)
Amount after year 3: \(\pounds6340.70 + \pounds177.54 = \pounds6518.24\)
Total amount of compound interest earned \(= \pounds6518.24 - \pounds6000 = \pounds518.24\)
Method 2
This is a much quicker method.
As the interest is going up by \(2.8\%\,p.a.\) this means that each year the amount is \(102.8\%\) of the previous year. Therefore:
\(102.8\% \,of\,6000\)
\(= 1.028 \times 6000\)
\(= \pounds6168\)
However, this only gives you the amount after year 1. To get the amount after year 3:
\({(1.028)^3} \times 6000\)
\(= \pounds6518.24\)
Now try this:
Question
Calculate the compound interest earned on \(\pounds8000\) at \(2.2\%\) per annum for 5 years.
\({(1.022)^3} \times 8000\)
\(= \pounds8919.58\)
Total amount of interest earned \(= \pounds8919.58 - \pounds8000 = \pounds919.58\)
Answer: \(\pounds919.58\)