1E - Compound Interest and Depreciation c
Key Concepts - What is this section all about?
The idea of repeated percentage change and the relationship with exponential functions and geometric sequences is what this is all about. What is often new at this stage is the idea of compounding periods that are more frequent than once a year. Compounding monthly, quarterly, etc, changes the effect and has a significant impact on the outcome. You'll need to build an understanding of the formula and how it can be used and then solve problems around the idea!
In this section you will learn about and practice,
- The concept of compound interest as repeated percentage increase and depreciation as repeated percentage decrease.
- Working with different compounding periods
- Understand the elements of the compound interest formula and how to use it to solve problems
- Learning how to use your GDC in different ways and, in particular the finance app to solve problems in involving the above
- Solve problems about depreciation as a context for repeated percentage decrease.
Read about it all at once for quick reference
The following slides outline the key points to know and understand about compound interest and include lots of worked examples. Here you can browse through all the explanations and slides at the same time. For more detailed video explanations see the 5 sections that follow. Open the hidden box to see.
Understand the impact of repeated percentage change
Here we look at understanding and carrying out compound interest calculations, how it works and what it means. Compound Interest is how it works in the real world. If you are saving money then each year the interest is calculated on an increasing amount and this works in your favour! Of course it works the other way around with dent too, but we'll get there.
Understand the impact of different compounding periods
Is 10% after 12 months the same as 5% after the first 6 months and 5% again for the next 6 months? No, its not, the second option gives you more because the 2nd time the interest is calculated it is calculated on a bigger amount. So if interest is ‘compounded semi annually’ this means is calculated twice a year like this. ‘Compounded monthly’ is even better. You only get a 12th of the interest, but you get it 12 times and it compounds every time! Open the hidden panel to see more!
Understand all the elements of the formula
The compound interest formula is a generalisation of all the things we have done so far. Once we understand all of the variables involved we can use it for all of the problems where we calculate the final value of an investment and understand the structure of that growth. Click on the hidden box for more!
Enter the calculator!
Your calculators all have a finance app that can do these calculations for you. This comes in to its own when you need to solve problems to find the different variables. When you need to find the interest rate or the present value and so on. These are not so easily done with the formula! Your GDC is a real life saver here, but you need to know and practise how to use it. Click to see more
Repeated percentage decrease
All this talk of savings compounding all the time is great, but lots of things depreciate too. For example, the value of a car depreciates year on year. The older it gets the less its worth. The effect is kind of the opposite. The amount it depreciates by gets less each year because the percentage is calculated on amount that gets smaller each time. This is the same principle but with percentage decrease. Click to see more.
Try out these online quizzes to see how well you understood the above! Rihgt click and open the quizzes in a new tab so you can refer back to help on this screen.
Compound Interest FV 1
Use this 16 question quiz for some quick fire practise and revision on the topic of Compound Interest where you are required to calculate the final value. Do these on the go on your mobile or at your...
Compound Interest FV 2
Use this 15 question quiz for some quick fire practise and revision on the topic of Compound Interest where you are required to calculate the final value. Do these on the go on your mobile or at your...
Annual Depreciation
Use this 16 question quiz for some quick fire practise and revision on the topic of annual depreciation. Do these on the go on your mobile or at your desk with a pen and paper by your side to help. Answer...
The following quizzes involve you using the finance app
Compound Interest - Solve for anything 1
Use this 15 question quiz for some quick fire practise and revision on the topic of Compound Interest where you have t solve for length of time, interest rate or present value. You will need to finance...
Compound Interest - Solve for anything 2
Use this 15 question quiz for some quick fire practise and revision on the topic of Compound Interest where you have t solve for length of time, interest rate or present value. You will need to finance...