We can use the compound interest formula to solve this problem:

Where:
- A = the future value of the investment ($6145)
- P = the initial deposit ($5000)
- r = annual interest rate (6.4% or 0.064)
- n = number of times interest is compounded per year (quarterly, so 4)
- t = number of years
Substituting the given values into the formula:

Now, we need to solve for t. Divide both sides by 5000 and then take the natural logarithm (ln) of both sides:

Now, isolate t by dividing both sides by
:

Now, plug in the values and calculate:

Rounded to the nearest hundredth, it will take approximately 3.18 years for the investment to grow to $6145.