How long will an investment take to quadruple its value at 10%/a compounded quarterly?

Question

a) determine an equation to describe this situation

b) determine the answer to this question and explain how you arrived at this solution.

Thx a lot i appreciate it!

Answer 1

a) 4 = 1.025^(# quarters)

b) # quarters = log 4/log 1.025 = 56.14 quarters

Answer 2

10% annual, compounded quarterly means:

(1 + .10/4)^t

we need to find t (time/number of quarters) such that:

Starting Value * (1 + .10/4)^t = Starting Value * 4

We can divide both sides of the equation by Starting Value to get:

(1 + .10/4)^t = 4

we need to solve for t, so, to isolate t, we take the natural log of both sides:

ln((1 + .10/4)^t) = ln(4)

t * ln(1 + .10/4) = ln(4)

t = ln(1.025) / ln(4)

t = 56.14 quarters = ~14 years