Answer:
We can use the formula for simple interest to solve this problem:
I = Prt
where I is the amount of interest earned, P is the principal (the initial amount invested), r is the annual interest rate (as a decimal), and t is the time (in years).
In this problem, we know that P = $6,000, r = 0.08, and I = $1,680. We want to find t, the time required to earn $1,680 in interest.
Substituting these values into the formula, we get:
$1,680 = $6,000 x 0.08 x t
Simplifying and solving for t, we get:
t = $1,680 / ($6,000 x 0.08) = 3.5 years
Therefore, it will take 3.5 years for $6,000 invested at 8% interest to earn $1,680 in interest.