Please explain the difference between compound and simple interest

First of all, let's start by defining the word 'interest'. Interest in mathematical terms generally means an amount of money that is accumulated over a period of time after an amount of money is invested or borrowed. For example: when you borrow money from a bank, you pay a small amount of money to them as a fee for them letting you borrow that money. This is called interest. Simple interest is calculated by working out the interest rate (r) over one time period, (for example one day) and then multiplying this result by the overall number of days (t). To do so we must know the original amount (p), interest rate (r) and the time period over which the interest needs to be calculated (t). The general formula for simple interest is: Interest (I)=Original amount (p) x Interest rate (r) x Time period (t). This means that simple interest rate calculates one fixed value of daily interest, and simply adds up the amount of interest over the amount of days it has accumulated, and the daily interest rate NEVER CHANGES.

Compound interest is slightly more complicated. The compound interest rate on a daily basis DOES change. Compound interest calculates the new interest every day of the original amount + the interest from the day before. For example, if I have £100 and a 5% daily interest rate, after one day the final amount will be (100 x 0.05) + 100 = £105. After two days, we now have to multiply the previous day's final amount by the interest rate to work out the new interest gained. So, we multiply £105 by 0.05 to work out the interest, then add this to £105 get £110.25. This can also be written as =Original amount x (Interest rate)^(Time period).