How do you find when a number is reached due to a percentage of growth?

Answer 1

Suppose you have a variable which grows at r% per period [year] and you want to find out how many periods, t, it will take before it grows, from a starting value of P to reach the value Q.

The approximate method used by younger pupils is trial and error. This is because the y do not have the necessary mathematical knowledge.

After t periods, the variable in question will have increased from P to Q where

Q = P*(1+r/100)t

then Q/P = (1+r/100)t

taking logarithms, log(Q/P) = log[(1+r/100)t] = t*log(1+r/100)

and so finally, t = log(Q/P) / log(1+r/100).