Find the time required for an investment of 5000 dollars to grow to 6900 dollars at an interest rate of 7.5 percent per year?

6900 = 5000 * (1 + ((7.5/100)/4))^(4t)
(1 + (0.075/4))^(4t) = 6900/5000
(1 + 0.01875)^(4t) = 1.38
1.01875^(4t) = 1.38
Since t is a real number, then 4t is a real number, so we have:
4t = log[1.01875](1.38)
t = log[1.01875](1.38) / 4
t =~ 4.3345824447998117178309133983688
So 4.25 years is not enough, so you'll have to wait until the next time the interest is compounded, which will be after 4.5 years.