At a certain fixed rate of compound interest per annum, how long it takes to generate an investment of 1 to n? Assume that only one amount is invested at the beginning of the time and no withdrawal is allowed.
n =1 * ( 1 + r )^t *(1 + r), solve for t, where n=FV, $1 =PV, r=Rate per annum, t=Number of years.
t =log(n / (r + 1)) / log(r + 1)
A slight adjustment in the formula given above, since whether at the beginning or at the end of a period, it makes NO difference in the final outcome for one lump sum payment. The "beginning" or the "end" of a period makes a difference ONLY with regard to "Periodic Payments". So, the above formula should be the stated as follows:
n = $1 x [1 + r]^t. Now, you can solve for "t"
t =log(n/$1) / log(1+r)
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