How long will it take $500 to double itself if it's invested at 8% annual interest rate compounded quarterly

Question

Set up and solve using an algebraic equation

If anyone can help me do this I will be very appreciative.

Answer 1

2 = (1 +.08/4)^4t solve for t

2 + 1.02^4t

take natural logs, naturally

ln2 = 4tln1.02

4t = ln2/ln1.02

t = ln2/4ln1.02 = about 8 3/4 years = doubling time

regardless of initial amount