compounded monthly word problem

Question

If you have $12000 in your money market account that is paying an annual interest rate of 12%, which is being compounded monthly, how many years will it take to double if the interest rate stays the same?

Answer 1

A = p(1 + r/n)^nt

24000 = 12000(1 + 0.12/12)^12t

2 = (1.1)^12t

ln 2 = ln (1.01)^12t

ln 2 = 12t ln 1.01

0.6931 ≈ 12t (0.009950)

69.6583 ≈ 12t

5.8≈ t

 

The investment shall double in approximately 5.8 years