The formula for continuous compounding is given by
A = P. [tex] e^{rt} [/tex]
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
[tex] 110000= 40000 . e^{(0.06.t)} [/tex]
[tex] \frac{110000}{40000} = e^{0.06t} [/tex]
[tex] 2.75= e^{0.06t} [/tex]
㏑(2.75) = ㏑[[tex] e^{0.06t} [/tex]]
㏑(2.75) = 0.06t
[tex] 1.0116 = 0.06t [/tex]
[tex] t= \frac{1.0116}{0.06} [/tex]
t= 16.86 years
The time taken for $40000 to amount to $110000 is 16.86 years
