What is r?

Anyway, i'll give you the general solutions and you can plug in r later.

In general, if interest is compounded n times per year, we use

A(t) = A0*(1 + r/n)^nt

where A(t) is the amount of money at any given time, A0 is the initial amount of money, r is the rate of interest, t is time, n is the number of times per year the money is compounded. Here goes.

We want A(t) = 2*A0 (since they said they wanted it to double), so we want

2*A0 = A0*(1+ r/n)^nt

=> 2 = (1 + r/n)^nt .........................divided both sides by A0

=> ln2 = ln(1 + r/n)^nt

=> ln2 = nt*ln(1 + r/n)

=> t = ln2/(n*ln(1 + r/n)), where t is the time in years.

a) Compounded monthly, => n=12

so t = ln2/(12ln(1 + r/12)) years

b) Compounded quarterly, => n=4

so t = ln2/(4ln(1 + r/4)) years

c) annually, => n=1

so t = ln2/ln(1 + r) years