OK, this one sounds complicated, but it’s really not. It’s a simple question, with a surprising answer. And a great lesson on the power of compound interest, for all of us.
The activity: 1p or £1000?
Ask if your child would rather be given £1,000 a day for 30 days, or start with a 1p, and double that penny every day for 30 days. Which one would leave them with more money? Work it out at 5 day intervals, then ask if they want to change their mind at each stage!
FYI, what happens is:
Not until day 22 do the 1p-ers start to beat the £1000-ers.
At the end of the 30 days…
…the 1p-ers have a whopping £5,368,709.12
…while the £1000-ers have a modest £30,000
Here’s the full breakdown for the 1p doubled everyday (the £1000 a day is a bit simpler to work out :)):
| Day | Amount |
| 1 | £0.01 |
| 2 | £0.02 |
| 3 | £0.04 |
| 4 | £0.08 |
| 5 | £0.16 |
| 6 | £0.32 |
| 7 | £0.64 |
| 8 | £1.28 |
| 9 | £2.56 |
| 10 | £5.12 |
| 11 | £10.24 |
| 12 | £20.48 |
| 13 | £40.96 |
| 14 | £81.92 |
| 15 | £163.84 |
| 16 | £327.68 |
| 17 | £655.36 |
| 18 | £1,310.72 |
| 19 | £2,621.44 |
| 20 | £5,242.88 |
| 21 | £10,485.76 |
| 22 | £20,971.52 |
| 23 | £41,943.04 |
| 24 | £83,886.08 |
| 25 | £167,772.16 |
| 26 | £335,544.32 |
| 27 | £671,088.64 |
| 28 | £1,342,177.28 |
| 29 | £2,684,354.56 |
| 30 | £5,368,709.12 |
Take it further
Firstly, instead of just revealing the numbers to your kids, you could get them to work it out – a good bit of math homework. Secondly, you could explain how compound interest works, and that effectively is what happens to the penny everyday. Use our Primer on ‘talking about compound interest’ here to help you.
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