The compound interest formula is:

Where:

From the question, we can deduce that P=$100, r=0.1, n=12, t=?, A=$175 and hence inserting the values into the formula gives:

- P = Principal amount (initial investment)
- r = Annual interest rate (as a decimal)
- n = Number of times the interest is compounded per year
- t = Number of years
- A = Amount after time t

Now, solve for and you will have the amount of years for the investment to grow from $100 to $175.