Final answer:
The balance due at the end of the first two years for a $6,000 loan with a 6% annual interest rate compounded continuously is $6,764.98.
Step-by-step explanation:
To determine the balance due at the end of the first two years for a $6,000 loan with a 6% annual interest rate compounded continuously, we use the formula for continuous compounding:
A = Pert
Where:
t is the time the money is invested for, in years.
Substituting the given values:
A = 6000 * e(0.06*2)
A = 6000 * e0.12
A = 6000 * 1.127497
A = $6764.98
Therefore, the balance due at the end of the first two years is $6,764.98.