Question

How long will it take $40,000 to grow to $110,000 if it is compounded continuously at 6%

Answer 1

The formula for continuous compounding is given by

A = P. $e^{rt}$

where P is the initial or principal amount = $40,000

A is the amount at the end =$ 110,000

r is the rate of interest = 6% = 0.06

t is the time = the value we need to find

lets plug in the values

$110000= 40000 . e^{(0.06.t)}$

$\frac{110000}{40000} = e^{0.06t}$

$2.75= e^{0.06t}$

㏑(2.75) = ㏑[$e^{0.06t}$]

㏑(2.75) = 0.06t

$1.0116 = 0.06t$

$t= \frac{1.0116}{0.06}$

t= 16.86 years

The time taken for $40000 to amount to $110000 is 16.86 years

Answer 2

You will need this formula:
Years = natural log (Total / Principal) / rate
Years = natural log (110,000 / 40000) / .06
Years = natural log (2.75) / .06
Years = 1.0116009117 / .06
Years = 16.86

Source:
http://www.1728.org/compint.htm
http://www.1728.org/rate2.htm