Final answer:
To calculate Mike's retirement account balance after 20 years with continuous compounding, use the formula A = Pe^(rt), where P is $7,692, r is 0.06, and t is 20. The calculation reveals the future value of the investment.
Step-by-step explanation:
Mike's investment of $7,692 in a retirement account at a 6% annual interest rate compounded continuously over 20 years can be calculated using the formula for continuous compounding, which is A = Pert. Here, P is the principal amount ($7,692), r is the annual interest rate (0.06), t is the time in years (20), and e is the base of the natural logarithm (approximately 2.71828). Plugging in the values, the future value A is calculated as:
A = 7692 * e(0.06*20)
Calculating this using a calculator or software that can handle exponential functions will give us the future value of the investment after 20 years.