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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.

Guest Nov 9, 2018

#1**0 **

**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) **

Guest Nov 9, 2018

#2**0 **

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)

Note: You may try this for yourself by using this online financial calculator:

https://arachnoid.com/finance/

Guest Nov 9, 2018

edited by
Guest
Nov 9, 2018