“Compound interest is the eighth wonder of the world. He who understands it, earns it ... he who doesn't ... pays it.”
- Albert Einstein
Yesterday, in my Principles of Food and Resource Economics class (135 students--mostly freshmanpeople and sophomores), I was talking about cost-benefit analysis. In particular, I was talking about comparing benefits and costs across time, which of course leads to a discussion of discounting. Rather than drone on about discount rates and present and future values, I decided to show the class the power of compound interest--if nothing else to provide them with something useful they might use outside of class (it's not like they will remember any actual material from class).
So here is the example I used: Suppose, starting at age 25, you invest $1,000 per year at 10% return per year (the rough long-term average of the S&P 500) until age 65. Alternatively, suppose you waited until age 45, but invested $2,000 per year for 20 years. In both cases you are investing $40,000. Which savings plan would you choose?
Most of the class chose the delay option (probably because we had already spent a good amount of time talking about the time value of money). I then showed them how to calculate the future value of an annuity (FV=$X(((1+r)^n)-1)/r).
In the first case, the future value of $1,000 ($X=$1000) invested at 10% annual interest (r=0.10) for 40 years (n=40) is $442,593. This seemed to shock most of the students. Investing $40,000 could multiply by over a factor of 10. I explained that is the power of compound interest.
To emphasize the point I then showed them that the future value of the second savings stream ($2,000 per year at 10% for 20 years) is 'only' $114,550. Again, this seemed to surprise many of the students.
So I asked the class, "What is the most sure way for you to become a millionaire by age 65?"
Someone shouted, "Marry rich!"
My job is done.
