Exponential Functions

Question

Find the time it takes for $6,600 to double when invested at an annual interest rate of 19%, compounded continuously.

_______ years?

 

 

 

Find the time it takes for $660,000 to double when invested at an annual interest rate of 19%, compounded continuously.

________years?

 

Answer 1

Amt at time =0 is $6600

Amt when doubled=$13200

A=pe∧rt

where A=amount after time t, p=amount to be compounded(initial deposit), r=annual continuous compound rate and t=time

A=$13200

p=$6600

r=19% or .19

Substitute:

13200=6600(e∧.19t)

divide both sides by 6600

2=e∧.19t

Take natural log of both sides 

Ln2=Ln(e∧.19t)

Ln2=.19t

divide both sides by .19

Ln2/.19=t

t=3.65 years