Episode 6: Exponential growth in Pensions

Taking Maths Further Podcast

This week the topic was exponential growth, and pension investments. We interviewed Simon Perera from Lane, Clark & Peacock about his work as an actuary, what an actuary is and how it involves predicting the growth of investments.

Interesting links:

• Actuarial science on Wikipedia
• Exponential growth on Wikipedia
• Exponential growth at Maths is Fun
• Be an actuary website
• The wheat and chessboard problem on Wikipedia
• Workplace pensions at Gov.uk

Puzzle: James has 250 friends on Facebook. He sees a really funny photo and sends it to two of his friends. The next day, each of those friends sends it to two of James’ other friends who haven't seen it yet. If this repeats, how many days will it take (including the first day on which James originally sent the photo) until all of James friends have seen it?

Solution:

It will take 7 days. The number of people doubles each day - so at the end of the first day, only 2 of James’ 250 friends have seen it, on the second day four of his friends have seen it, on the third day 8 friends, on the fourth day 16 friends, and so on until on the 6th day, when the number of friends who have seen it is 128. This means on the seventh day, the remaining 122 friends will also be sent the picture.

This isn’t a hugely realistic model - firstly, websites like Facebook allow you to send things to all your friends at once so it’s not clear why you’d do it two at a time; but also, it’s not necessarily plausible that people will always send it to people who haven’t seen it before, so the way things like this spread in reality isn’t always as fast as this - some people may be counted twice if it’s sent to two random people per day.

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