The Rule of 70: Suppose you have a variable, called Y, that grows at a constant rate g. The value of the variable at time t + h in relation to its value at time t is then: Yt+h = (1 + g)^h * Yt This problem will ask you to work on demonstrating a useful result called the "rule of 70". In particular, we want to find an expression for the number of periods, h, required for a variable to double.

(a) The rule of 70 states that the number of years it takes for a variable to double is approximately 70 divided by the growth rate expressed as a percentage. If the variable grows by 2% per year, that would mean g = 0.02, and the rule of 70 would indicate that the number of years it takes for the variable Y to double is approximately 70/(100g). Show how the rule of 70 is derived (hints: take logarithms and use the approximation ln(1 + g) g).

(b) According to the rule of 70, how many years would it take for a variable to double if that variable grows at annual rates of 2, 5, 7, 10, and 20%?

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Deriving the Rule of 70 a We want to find the number of periods h required for a variable Y to doubl... View the full answer