Compound interest question:

Question

When Aaron invested $100 at 4.5% p.a. annually compounding, it amounted to $142.21. For how many years was it invested?

Is there a way to solve this question without using the formula for compound interest?

Answer 1

You could repeatedly divide by 1.045 until you reach appr 100

e.g.
142.21/ 1.045 = 136.086 -- once
136.086/1.045 = 130.2256 --twice
....
109.20/1.045 = 104.50 -- 7 times
104.50/1.045 = 100 -- 8 times

so it took 8 years