Math - Investments

If the interest is compounded continuously
The Formula is
FV = PeYr
where P is the starting principal and FV is the future value after Y years.
Now
P=1000, FV=1000000
1000000=1000e0.1Y
1000=e0.1Y
ln1000=0.1Y
Y=69.0775528
So, to the nearest year, it will take 70 years for me to become a millionaire if I invest 1000 at 10% interest compounded continuously

To get the formula we'll start out with interest compounded n times per year:

FVn = P(1 + r/n)Yn

where P is the starting principal and FV is the future value after Y years


1000000=1000(1+10%)^n

1000=1.1^n

log1000=nlog1.1

n=3/log1.1
= 72.48 yrs

round up to 73Years

You need 73Years to be a millionaire if I invest 1000 at 10% interest compounded continuously