Here’s a brain teaser I like to give to my class:
Dan and Stan are both 20 years old and will retire in 40 years. Stan starts investing when he is 20 and deposits $2,000 at the end of each year into an account paying 10%. Stan stops when he turns 30. In contrast, Dan starts when he is 30 and would like to make end of the year deposits into an account earning 10%. How much will Dan have to save each year in order to catch up with Stan?
Here’s the answer:
Stan invests for 10 years, so at the end of that period, Stan’s contributions plus return are equal to approximately $31,875. Stan contributes no more but that amount grows to $556,197 by the time Stan retires. This is the number Dan must accumulate.
Dan achieves this by depositing an amount for thirty years into the account. The amount he must deposit is $3,381 per year. Remember, he must deposit that amount for thirty years!
Moral of the story? Save early, save often!