I think there’s insufficient info, because we don’t know whether it’s simple or compound interest. And, if it’s compound, is interest compounded daily, monthly, quarterly, annually or continually? The time limit varies considerably between these types. An answer can be given if interest is compounded continuously (the highest growth type). The formula for continuous compound interest is A=Pe^(rt) where r=rate per period, t=number of time periods, P=principal, A=amount after t time periods.

If t=number of months and r=monthly rate we have a series. If the monthly payment is m, then the first monthly payment becomes me^rt after t months. The second monthly payment becomes me^(r(t-1)) after one fewer months than the first payment. The last payment has only a month’s continuous compound interest.

The series is me^r(1+e^r+e^(2r)+...+e^(r(t-2))+e^(r(t-1)).

This can be written as a geometric progression: me^r(e^(rt)-1)/(e^r-1).

This sum needs to grow to $1000000, so:

500e^(0.205/12)(e^(0.205t/12)-1)/(e^(0.205/12)-1)=1000000.

e^(0.205t/12)-1=1000000(e^(0.205/12)-1)/(500e^(0.205/12)).

e^(0.205t/12)-1=33.8765 approx. e^(0.205t/12)=34.8765.

Taking logs: 0.205t/12=ln(34.8765).

t=12ln(34.8765)/0.205=207.91 months=17.33 years approx.

So Rodd can realise a growth to $1,000,000 in about 17 years 4 months, if continuous compound interest is permitted.

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