Compound Interest

I recently read a debate between two colleagues who disagreed on the math topics that should be taught to high school students. The essence of the disagreement boiled down to classical topics versus practical. I'll offer one topic of practical importance that should be emphasized, compound interest. Understanding the power of compound interest over long period of times makes the difference of wealth accumulation versus debt accumulation. 

Interest rates for savers are currently very low, but just two or three years ago, I bought a 5-year CD with 3.3% interest. The power of compound interest is that one earns interest on the principal and on the earnings. Simplified at bit, $100 becomes $103.30 after one year. After 5 years, the initial investment becomes: $100 x (1.033) x (1.033) x (1.033) x (1.033) x (1.033) = $117.63. That is a bit more than the $116.50 that would have been earned under a simple interest arrangement ($100 x 5 x 1.033). 

On the debt-accumulation side, things are much worse as credit card companies are not generous in their terms to consumers. Consider a debt of $100 carried for 5 years at the 18%. This debt now becomes, $228.78.

The amount by which the debt or the asset grows depends on two key things, the interest rate and time. Above we saw how the grow varies by interest rate, but time becomes a big factor especially when long periods of time are involved.

For a final example, let's look at the purchase of Manhattan. This week marks the 396th anniversary of when Dutch settlers traded $24 dollars worth of trinkets in exchange for the now, very valuable, New York real estate. Had the sellers been able to invest in a 396-year certificate of deposit, what would their proceeds be worth now? That would be $24 times (1.033) x (1.033) ... x (1.033) or $24 x (1.033) raised to the power of 396 which now would be $9,203,194. The investments didn't exist at the time, but one with a very long-term time frame would be told by financial advisors to invest in something with more risk, like stocks. The last sixty years or so, the S&P500 index has yielded about 8%. An investment at 8% over four centuries becomes astronomical so for the final calculation, let's back that average to 6.5%. The $24, if invested in 1624, would now be worth $24 x (1.065) ^ 396 = $1.6 trillion. A search for the current value of all Manhattan real estate revealed the current value to be approximately $1.74 trillion.