# Answer To The Howard Hughes Rate of Return Test

People are not intuitive about compound interest problems so  you need to learn a way to approximate rates of return.

On Friday I presented this problem.

Howard Hughes inherited \$400,000 and died 53 years later worth \$2,000,000,000.  What was his average rate of return?

There are several ways to solve this with a calculator or a computer.  And, there is at least one way to solve it without those tools.  All start with the realization that he ended with 5,000 times more.

My financial calculator using PV=1, FV=5000, PMT= 0, N=53 computes i to be 17.433468%

Using Excel Create A = LN(5000)/53;  Interest rate = EXP(A)-1 = 17.433468%

Or we can get a good guess this way. Use the handy Rule of 72

First, find out how many doubles there are.  5,000 lies between 2 to the power 12 (4096) and 2 to the power 13 (8192).  Around 12.3 doubles. So each double took about 4.31 years.

We also know that if you divide the number of years it took to double into 72 you get an approximate interest rate.  In this case 16.7%.  It also works the other way.  If you know the interest rate, it will tell you how long to double.

Was your guess close to 17%?

If not, be sure to do the arithmetic in future.  Your intuition may fail you.

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