To solve this we are going to use the compound interest formula 
where:
is the investment
is the interest rate in decimal form
is the number of times the interest is compounded per year
is the time in years
is the amount after years
First, lets convert the interest rate to decimal dividing it by 100%:
Next, lets find. Since we know that the interest is compounded every 4 months (quarterly), it will be compounded 
times in a year, so 
.
We also know that
and 
, so lets replace all the quantities into our compound interest formula:
Notice that the the number of years is in the exponent, so we have to use logarithms to bring it down. But first lets divide both sides by 16000 to isolate the exponential expression:
Now that we know, the last thing to do is convert 0.43 years to months:
We can conclude that Jimmy's investment will take 6 years and 5 months to reach $25,000.
where:
First, lets convert the interest rate to decimal dividing it by 100%:
Next, lets find
We also know that
Notice that the the number of years
Now that we know
We can conclude that Jimmy's investment will take 6 years and 5 months to reach $25,000.