text: how long wiil it take a given sum of money (say. in rupees) to increase 4 times its present value when? compounded half yearly at 7% rate of interest? the formula for determining compound interest is: at = ao (1 + r/n)^(n*t)  to determine how long it takes your money to double, use the following: at = 2 = amount at time t ao = 1 = amount at beginning r = .07 (7%) = rate of interest n = 2 = number of times compounded yearly  at = ao (1 + r/n)^(n*t) 2 = 1 * (1 + .07/2)^(2t) 2 = 1.035^2t log 2 = 2t log 1.035 log 2 / log 1.035 = 2t t = (0.30103 / 0.01494) / 2 = 10.07 years (solution)  check: at = ao (1 + r/n)^(n*t) 2 = 1 * (1 + .07/2)^(2*10.07) 2 = 1.035^20.14 2 = 1.9994 (close enough!)  now, for the above formula, to find t, given the other values: at = ao (1 + r/n)^(n*t) at / ao = (1 + r/n)^(n*t) log (at / ao) = (n*t) log (1 + r/n) n * t = log (at/ao) / log (1 + r/n) t = log (at/ao) / n log (1 + r/n)