Final answer:
The interest earned on $80,000 deposited into an account with a 7.5% interest rate compounded continuously after one year is approximately $6,237.60. The closest answer choice is B) $6,200.
Step-by-step explanation:
When determining the interest earned on $80,000 deposited in an account paying 7.5% interest compounded continuously, we use the formula for continuous compound interest, which is A = Pert, where P is the principal amount, r is the annual interest rate, t is the time in years, and e is the base of the natural logarithm.
For this question, P is $80,000, r is 0.075 (because 7.5% as a decimal is 0.075), and t is 1 year. So our formula looks like this: A = $80,000e0.075(1).
Using a calculator, we find that e0.075 is approximately 1.07797. The total amount in the account after one year is $80,000 × 1.07797, which equals approximately $86,237.60. Finally, to find the interest earned, we subtract the original principal from the total amount: $86,237.60 - $80,000 = $6,237.60.
Answer choice B rounds this to $6,200, which is the closest to the actual interest earned after the first year.