Explaining simple and compound interest

In the run up to exams simple and compound interest is something on the list that a couple have asked about, so I thought I’d do a quick recap now.  

There are 2 forms:

Simple interest:

Clara invests £300 for 4 years in an account where she will earn 5% simple interest. How much will be in her account at the end of the 4 years?  

£300 = 100% of the value  

(divide by 100 to find 1%)

£3 = 1%

(multiply £3 by 5 to work out what 5% is)

£15 = 5%  

With simple interest, each year they will give her another £15. If she keeps the money in the account for 4 years, they will give her 4x £15 (£60).  

If we add this on to her initial investment of £300, we can work out the amount that is in her account at the end of the 4 years:  

£300+£60 = £360  

The other interest type is Compound interest.  

This time the amount of interest is calculated as a percentage of the money that is in the account.  

So, if J invests £300 for 4 years in an account where he will earn 5% compound interest. How much will be in his account at the end of the 4 years?  

This style just has one basic formula to learn:  

£300 x 1. 05^4  

We start with the £300 this is the initial investment.

We then multiply by 1: because it is an investment, he will get the initial investment back as well as the additional interest.

The 1 signifies the whole initial investment.

The .05 is the percentage rate.

It is .05 because we are multiplying by just 5% rather than 50%. (If it was 2.5% we would multiply by 1.025)

Finally, the power of 4 represents the 4 years that he will be investing the money for.  

If we type this into the calculator we should get the answer: £364.65

So, in this instance J receives a slightly better return on investment than Clara.  

That really was a simplified version of interest, but I hope it made sense.