The number of years n required for an investment at interest rate r to double in value must satisfy (1 + r)n = 2. Using ln 2 = .69 and the approximation ln(1 + r) ≈ r valid for small r, show that n ≈ 69/i, where i is the interest rate percentage (that is, i = 100r). Using the better approximation ln(1+r) ≈ r − 1 2 r2, show that for r ≈ .08 there holds n ≈ 72/i.

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