interest rate?

Question

suppose you invest 5,000 dollars and would like your investment to grow to 10,000 in eight years. What interest rate, compounded weekley, would you have to earn in order for this to happen?

Please show how you did the problem.

Answer 1

Let interest rate be r

10000 = 5000(1+r/100)^417
or 2 = (1+4.17r)
or 4.17r = 1
or r = .239 %

Answer 2

Let´s suppose that there are 52 weeks per year(Really there is one day more per year) so you´ll have 8*52+1 weeks in 8 years

calling x the interest rate per week

10.000=5.000(1+x)^417 so 2= (1+x)^417 and (log2)/417= log(1+x)

which gives you x= 0.0017 which coresponds to a yearly interest rate of 9.03%