So there are two twins – let’s call them Jacqueline-Joyce and Josephine-Jae. Both girls are blonde, financially conscious, and dislike it when you address them by an abbreviated version of their name. At the age of 25, both Jacqueline-Joyce and Josephine-Jae land jazzy jobs juggling jade jewels for the Jacksonville Jaguars. (This is precisely why this franchise does not make any money.) What follows next is very important, so pay attention. At 25 – the very same year she embarks on her illogical career down in Florida – Jacqueline-Joyce begins investing $3,000 a year into a Roth IRA. She continues to invest each year until she turns 35, and then never invests in her Roth IRA again. Josephine-Jae, on the other hand, caught up in all the Jacksonville Jaguars excitement, doesn’t remember to begin investing in her Roth IRA until she turns 35. But once she does begin investing, Josephine-Jae invests $3,000 a year, every year, until she turns 65. Now, the question for you is this: If you assume a constant return – let’s call it 7.5% a year regardless as to whatever wacky things are going on in the world – who has more money in her Roth IRA when she retires from juggling jewelry at 65?
Is it Jacqueline-Joyce, who invested $30,000 over the first ten years of her career? Or is it Josephine-Jae, who invested $90,000 over the last thirty?
Is your mind blown? I know ours were. But after we pieced our scattered brains back together, we set out to determine what sorcery could have possibility fostered such an unlikely outcome. As it turns out – that sorcery? It was just math. You see, without going all high school algebra teacher on you, the phenomena revealed in the Paradox of the Twins is explainable entirely through the Law of Compounding Interest. Briefly put, the Law of Compounding Interest states that by investing your money at a certain yearly rate, not only will your initial investment grow at the predetermined percent, but the yield from your initial investment will grow at that rate as well. So if you invested $100 at the abovementioned 7.5% per year, after year one you’d have $107.50 – a gain of $7.50. But rather than making that same $7.50 in year two (7.5% of $100), your gain would instead be 7.5% of $107.50 ($8.06). And in year three, it would be 7.5% of $115.56, and so on.
So by the time Josephine-Jae gets around to investing, Jacqueline-Joyce’s Roth IRA nest egg is already appreciating at more than $3000 per year – $3,183.25 to be exact. Therefore, it would be impossible for Josephine-Jae to catch Jacqueline-Joyce at her current $3,000 per year rate – even if she did invest three times the money over triple the amount of time.