1. (The 72 rule) The number of years n required for an investment at interest rate r to double in value must satisfy (1 +r)" = 2. Using In 2 = 0.69 and the approximation In(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 In(1 +r) ~ r - 2, show that for r ~ 0.08 there holds n ~ 72/i