How to Become a Billionaire

Algebra Level 3

Warren Buffett, one of the wealthiest men on earth, had a net worth of about $6,000 at age 15. By the year 2013 (age 83), his wealth grew to $60,000,000,000. The compound growth rate over the period was approximately $\text{\_\_\_\_\_\_\_}$ per month .

Note: Don't use a calculator. Use the following log values, if necessary: $\begin{aligned} \log 1.20 &=0.079\\ \log 1.15 &=0.061\\ \log 1.10 &=0.041\\ \log 1.05 &=0.021\\ \log 1.03 &=0.013\\ \log 1.02 &=0.009\\ \log 1.01 &=0.004. \end{aligned}$

1 % 2 % 3 % 5 % 10 % 15 % 20 %

1 solution

Jimin Khim Staff
Sep 12, 2017

Let $x$ denote the compound monthly growth rate. Then $\begin{aligned} 6000\times (1+x)^{12 \times (83-15)} &=6000\times (1+x)^{12 \times 68}\\ &=6000\times (1+x)^{816}\\ &=60000000000\\ \Rightarrow (1+x)^{816}&=10000000\\ \log(1+x)^{816}&=\log 10000000\\ 816\times \log(1+x)&=7\\ \log(1+x)&=\frac{7}{816}\approx 0.009. \end{aligned}$ Therefore, since $\log 1.02=0.009$ from the above note, we have $1+x=1.02 \implies x=0.02=2\%.$

While using logarithmic tables was an important method until about 30 - 40 years ago, scientific calculators give a much more accurate value for the 816th root. (E.g. my vintage 20+ years old (the model itself could be around 25 years old, and probably wasn't the first with this capability) Casio calculator gives me the following value for (1 + x): 1.019948941 ).

Zee Ell - 3 years, 9 months ago

How to Become a Billionaire

1 solution

0 pending reports