Aaron is investing $6700 of his savings from his summer job. He can choose between simple interest at 6% and compound interest at 5%. Aaron wants to take advantage of the higher interest rate of the simple interest option. At most for how many years should Aaron invest his summer job savings to gain more with simple interest before compound interest at 5% becomes more financially beneficial?
Let x be the number of years Aaron should invest his summer job savings.
After x years, the amount of money Aaron will earn with simple interest is 6700 * 0.06 * x = 402x.
After x years, the amount of money Aaron will earn with compound interest is 6700 * (1 + 0.05)^x = 6700 * 1.05^x.
To find the maximum number of years, we need to solve the following inequality: 402x > 6700 * 1.05^x.
Dividing both sides of the inequality by 6700 gives 0.06x > 1.05^x.
Taking the logarithm of both sides of the inequality gives log(0.06x) > log(1.05^x).
Using the properties of logarithms, we can rewrite the inequality as x * log(0.06) > x * log(1.05).
Subtracting x * log(1.05) from both sides of the inequality gives x * (log(0.06) - log(1.05)) > 0.
Since log(0.06) - log(1.05) is negative, we can divide both sides of the inequality by (log(0.06) - log(1.05)) without changing the inequality: x > 0 / (log(0.06) - log(1.05)).
Simplifying the right side of the inequality gives x > 0 / (-0.2218).
Since dividing by a negative number flips the inequality sign, we have x < 0.
Therefore, Aaron should invest his summer job savings for less than 0 years.
Since investment periods cannot be negative, Aaron should invest his summer job savings for 0 years.
Therefore, compound interest at 5% is financially beneficial from the start. Answer: \boxed{0}.