I need some help working out this problem.

Question

How many years will it take for a $100 investment to grow to $700 if it is compounded continouslly at a rate of 9%?

Formula = A(t) = P * 3^rt

Answer 1

Step 1:

Find the time by using continuous compounding formula:

A = P * e^(rt) 

Here,
P = principal 
r = rate per period 
t = number of periods in years

Substitute 700 for A,100 for P, and (9/100) =0.09 for r.

700 = 100 * e^(0.09 * t) 
7 = e^(0.09 * t) 
ln(7) = 0.09 * t 
t = ln(7) / 0.09 
t = 21.62 years

Solution:

Number of periods are 21.62 years