The rule is:



We will assume the interest accrues once yearly, so n = 1

and the formula becomes





So for Steven, P = 2000, so the amount A, in t years, is



Steven's GIC doubles every five years,
So we substitute t = 5, and A = 4000 (double 2000),
so we can solve for r:



Divide both sides by 2000



Take the 5th root of both sides:



Simplifying the right side:



Solving for r:



Substituting that into





or



This is the formula for Steven's amount A in t years.

---------------------------------------------

Now we do exactly the same thing with Dana's
GIC.



Now for Dana, P = 1000, so the amount A, in t years, is



DANA's GIC triples every three years,
So we substitute t = 3, and A = 3000 (triple 1000),
so we can solve for r:



Divide both sides by 1000



Take the cube root of both sides:



Simplifying the right side:



Solving for r:



Substituting that into





or



This is the formula for Dana's amount A in t years.

-------------------------------

So to find out when they have an equal amount, we

set their two A's equal, and solve for t:

 and 



Divide both sides by 1000



Change the roots to fractional exponentials of their radicands:

 = 

Multiply inner exponents by outer exponents

 = 

Write the first  as 

 = 

Change the exponent  to  so you 
can add exponents on the left:

 = 

Add exponents:

 = 

 = 

 = 

Raise both sides to the 15th power

 = 

Multiply inner exponents by outer exponents:

 = 

Cancel 5 into 15 on left and 3 into 15 on the right:

 = 

 = 

Take the log (either log10 or ln) of both sides

 = 

Use the rule of logs 

 = 

Replace  by  and replace  by 

 = 

 = 

 = 

Isolate the terms in t on the right

 = 

Factor out t on the right:

 = 

Divide both sides by 

 = 

Now replace  by  
and replace  by 

 =   

Use calculator to get right side

 = 

So the answer is just after 3 years.

Edwin