Question

Suppose that 2400 is invested at an interest rate of 2 %per year, compounded continuously. After how many years will the initial investment be doubled?

Answer 1

A(t) = P e^(rt)

A = total money after t years
P = initial investment
r = rate
t = time

A = 2x
P = x
r = 0.02
t = ?

2x = x e^(0.02t)
2 = e^(0.02t)
ln 2 = 0.02t
\[\frac{\ln2}{0.02}= t\]