how long will it take to acquire 1,000,000 with the principle of 10,000 at 10% interest compounded continuoustly?

how long will it take to acquire 1,000,000 with the principle of 10,000 at 10% interest compounded continuoustly?

It will take: 46.05 years for $10,000 to grow to $1,000,000 @ 10% comp.continuously. 10% comp. continuously=10.517091808 compounded annually. The formula you would use to calculate it is this: FV=PV(1+R)^N, where FV=Future value, PV=Present value, R=Interest rate per period, N=Number of periods.

You have to use logs to solve for N in this particular problem.

Equation: A=Pe^rt, where A is the total, P is the principle, r is rate, and t is time

1,000,000=10,000e^(.1)(t)

Divide both sides by 10,000 and multiply .1 and t

ln(100=e^.1t) 

ln and e are inverses, so convert e to ln to bring t into a usable form

ln100=.1t

from here just isolate t and solve

1,000,000 = 10,000e^(.1t)   divide both sides by 10,000

100  = e^(.1t)    take the natural log of both sides

ln (100)  = ln (e)^(.1t)    and we can write

ln (100)  = (.1t) ln e     and ln e = 1   so we can ignore this

ln(100)  = .1t        divide both sides by .1

t = about 46.05 years