What it shows
Two formulas grow the same sum at the same rate, one adding the same interest each year and one adding interest on interest. The chart shows compounding pulling ahead with time.
The science
Simple interest is P x r x n / 100 and grows in a straight line. Compound interest earns interest on the interest already added, so the amount after n years is P x (1 + r/100) to the power n, which curves upward. The gap grows slowly at first and then faster, which is why starting to save early matters. The spreadsheet function FV gives the same compound result.
Materials
Cost: free. Many items come from home or from waste; spare parts such as LEDs, motors and wire are in the store.
- A computer, laptop or phone with a browser (free)
- A spreadsheet program: LibreOffice Calc (free) or Google Sheets (free)
- A made-up amount, for example Rs 10,000 at 8 percent a year (use rates from a bank notice board for real values)
- A notebook and a pencil
Safety
This project uses safe, everyday materials. Still, read the rules below with a parent before you start.
Never use mains electricity: power models with cells, batteries or a low-voltage adapter. Sharp and hot tools, flames and lab chemicals need an adult or your teacher beside you. Keep magnets, button cells and small parts away from young children, and wash your hands after making.
All the safety rulesStep by step
8 steps. Do them in order, and test each part before you go on to the next. Write what you notice in a notebook as you go.
In A1 type Principal and B1 10000; in A2 type Rate percent and B2 8.
In A4 to D4 type headings Year, Simple, Compound, Gap.
Fill A5 to A25 with years 0 to 20 (type 0 and 1, select both and drag the fill handle down).
In B5 type =$B$1+$B$1*$B$2*A5/100 and copy down for the simple amount.
In C5 type =$B$1*(1+$B$2/100)^A5 and copy down for the compound amount.
In D5 type =C5-B5 and copy down, then check C25 with =FV(B2/100,20,0,-B1) which should give the same number.
Select A4:C25, insert a Line chart and add the title Simple against compound interest.
Change the rate to 12 and the principal to 5000 and describe how the two lines move.
What you should see
The two lines start together; the simple line is straight and the compound line curves above it. After 20 years Rs 10,000 at 8 percent is about Rs 26,000 simple and about Rs 46,610 compound.
Viva questions
A teacher or a judge will ask how it works. Try to answer each question before you open it, then compare.
1What is compound interest?
Interest that is also earned on the interest already added.
2Why does the gap widen with time?
Each year’s interest is on a bigger amount, so it grows faster.
3What does the ^ sign do?
It raises a number to a power.
4Why use $B$1?
The dollar signs keep the cell fixed when the formula is copied down.
Take it further
Add a column for compounding every six months, using (1 + r/200)^(2n), and compare.
Change one thing, measure what happens, and add a table or chart of your readings: that is what turns a model into your own investigation.
Free ebooks for this project
Computer & office
MS Excel Study Book
The complete study notes, practice questions and glossary for MS Excel
Computer & office
Excel Formulas Workbook
Sixty formulas and functions, each with a worked example from school, shop or office