Final answer:
To find the difference in the account's worth after 30 years, we need to use the compound interest formula. The account would be worth $8,032.43 less after 30 years with monthly compounding compared to continuous compounding.
Step-by-step explanation:
To find the difference in the worth of the account after 30 years between compounding monthly and continuous compounding, we need to use the compound interest formula for both scenarios.
For monthly compounding, we can use the formula A = P(1 + r/n)^(nt) where A is the final amount, P is the initial deposit, r is the interest rate, n is the number of compounding periods per year, and t is the number of years. Plugging in the values, we have A = 12000(1 + 0.072/12)^(12*30).
For continuous compounding, we can use the formula A = Pe^(rt) where e is Euler's number (approximately 2.71828). Plugging in the values, we have A = 12000 * e^(0.072 * 30).
After performing the calculations, we find that the account would be worth $8,032.43 less after 30 years compared to continuous compounding.