Final answer:
Using the formula for continuous compounding, A = Pert, with an initial deposit of $12,000, an annual interest rate of 7.2%, and a time span of 30 years, the investment would be worth approximately $103,912.08, which does not match any of the provided options.
Step-by-step explanation:
To calculate the future value of an investment account with continuous compounding, you use the formula A = Pert, where P is the principal amount ($12,000), r is the annual interest rate (7.2%), and t is the time in years (30 years). The constant e is approximately 2.71828, which is the base of the natural logarithm.
Plugging the values into the formula gives us:
A = 12000 * e(0.072*30)
Performing the calculation:
A = 12000 * e2.16
A = 12000 * 8.65934004 (using a calculator for e2.16)
A ≈ $103,912.08
However, none of the provided options matched this calculation. It seems there might have been a misunderstanding in the question or the options given do not account for continuous compounding. For continuous compounding, the correct answer would be none of the options above.