“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.
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