Basic math question about compounded interest

Question

Bank A provides a curious financial instrument: a savings account that yields a complex interest rate r = -1 + 2i per year (where i is the imaginary unit, satisfying i² = -1). John deposited U$1 in his savings account today. Assuming the interest is compounded annually, what is the amount of time (in years) that John must wait before he has $16 in his savings account?

a) t = 1

b) t = 2

c) t = 4

d) t = pi

e) t = e

Answer 1

Using the formula: A = P(1+r)^t

16 = 1(1-1+2i)^t

16 = (2i)^t since i⁴ = 1, raise both sides to the power of 4

16⁴ = (2i)^4t

16⁴ = 16^t

Therefore t = 4