# Math

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If you deposit 1200.00 annually with 5% compounded interest, how many years will it take to get to a million dollars?

• Math -

Assuming interest is compounded annually (yearly) at r% starting from an initial amount P, then the compound interest formula gives the final amount A after n years.
A=P(1+r/100)^n
For the given case
1000000=1200(1.05)^n
Rearrange:
(1.05)^n=1000000/1200=1000/1.2
Take log on both side
n(log 1.05)=log (1000/1.2)
Solve for n
n=log(1000/1.2)/log(1.05)
=137.84 (approx)
or about 137 years and 10 months.
Not forgetting that we all will probably be making a million dollars a month by then.

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