Suppose you want to invest $10,000 in stocks, and want it to grow to $50,000 in 20 years. what annual interest rate must the stocks grow at?

  about 8.4%

Step-by-step explanation:

You want to find r such that ...

  10,000×(1 +r)^20 = 50,000

  (1 +r)^20 = 50,000/10,000 = 5 . . . . . divide by 10,000

  1+r = 5^(1/20) . . . . . . . . . . . . . . . . . . . . take the 20th root; then subtract 1

  r = 5^(1/20) -1 ≈ 0.083798 ≈ 8.4%

The stocks must grow at an annual rate of 8.4%.

Some calculators will take a root other than 2 or 3. For other calculators, you need to use a fractional exponent or use logarithms.

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