The miracle of compound interest

In reading my monthly MoneySense magazine I relearned the genius of compound interest. It is used as a way to encourage people to save because growth on money compounds, with most of the growth occurring in the latest stage, ie. the time closest to retirement. The concept is so powerful that when asked what the most powerful force in the universe is, Albert Einstein replied "compound interest". So I thought I'd revisit this concept for readers.

In his great book, RRSPs, Preet Banerjee extols the virtues of compound interest by giving a scenario in which you are offered a large lump sum of money for a month's work, or the chance to be paid $0.01 one day, but your pay will double every day for a month. Of course, at the end of the month, the guy who took the lump sum looks like a sucker because the doubler made WAY more money! But I thought to myself, whose money ever doubles in a savings regimen? 5 or 10% seems much more realistic.

I'm going to give you 2 scenarios. In both, assume that you'd had enough money saved up prior to starting this job to hold the whole year through so pay frequency does not come into the equation as a confounding factor.

1. For 1 year of work, 365 days solid with no breaks, I will pay you $5 000 000.

2. For 1 year of work, 365 days solid with no breaks, I will pay you $0.01 on the first day. Every day after that I will increase your wage by 5%.

What do you choose?

If you choose scenario 1, you will make roughly $416 667 a month, or $2.5 million after 6 months.

If you choose scenario 2, after 1 month, you will have made a whopping $0.66. Month 2? $3.54
Month 6? $1303.28

Starting to look like scenario 2 man is a big donkey.

Month 8? $25565.11
Month 10? $454 799.03

Only 2 months to go, and he's nowhere near the $5 million mark. What a moron.

Month 11? $1 965 615.85

At the end of the year, scenario 2's total earnings are...........$10 842 368.12

The key here is that most of the growth did not occur until very late in the year. In fact, at what point did scenario 2 surpass scenario 1? Day 350!!!! There are only 15 days left in the year, but in those 15 days alone, the money grows by another $5 million.

Even if snopes.com says the attribution of the aforementioned quote to Albert Einstein is likely a modern creation, whoever wrote it or said it is on to something.