If I invest 10 000$ and average an interest return of 2% every month, how many years will it take before I get to 1 000 000 $ ?

If I invest 10 000$ and average an interest return of 2% every month, how many years will it take before I get to 1 000 000 $ ?

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We have

A_^t = A₀(1 + r)^12t

Where:

A_t = amount accumulated at the end of some time  (in our case, $1 000 000)

A₀ = Amount invested ($10 000)

r = interest rate expressed as a decimal  (.02)

12 = compoundings per year

t = time in years (what we're looking for)

So we have

1000000 = 10000(1 +.02)^12t         .........let's divide both sides by 10000

100 = (1.02)^12t                             .........now, take the the "log" of both  sides

log (100) = log (1.02)^12t                ........by a "log" property, we can bring the 12t "out front" on the right

log (100) = (12t) log (1.02)            ........divide both sides by log (1.02)

log (100) / log (1.02) = 12t             ........divide both sides by 12

log (100) /(12 log (1.02)) = t     =      about 19.38 years