Question: 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?

Answer: The formula for determining compound interest is:\nAt = Ao (1 + r/n)^(n*t)\n\nTo determine how long it takes your money to double, use the following:\nAt = 2 = amount at time t\nAo = 1 = amount at beginning\nr = .07 (7%) = rate of interest\nn = 2 = number of times compounded yearly\n\nAt = Ao (1 + r/n)^(n*t)\n2 = 1 * (1 + .07/2)^(2t)\n2 = 1.035^2t\nlog 2 = 2t log 1.035\nlog 2 / log 1.035 = 2t\nt = (0.30103 / 0.01494) / 2 = 10.07 years (solution)\n\nCheck:\nAt = Ao (1 + r/n)^(n*t)\n2 = 1 * (1 + .07/2)^(2*10.07)\n2 = 1.035^20.14\n2 = 1.9994 (close enough!)\n\nNow, for the above formula, to find t, given the other values:\nAt = Ao (1 + r/n)^(n*t)\nAt / Ao = (1 + r/n)^(n*t)\nlog (At / Ao) = (n*t) log (1 + r/n)\nn * t = log (At/Ao) / log (1 + r/n)\nt = log (At/Ao) / n log (1 + r/n)
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