Final answer:
To determine the difference in the future value of investments for Brandon and Julian, one with continuous compounding and the other with monthly compounding, we use respective formulas. With the known investment amount, interest rates, and duration, we apply formulas to calculate future value and then subtract Brandon's future value from Julian's to find the difference. Julian's account, with a higher rate and more frequent compounding, is likely to have more funds than Brandon's.
Step-by-step explanation:
To calculate how much more money Julian would have in his account than Brandon after 18 years, we need to apply the formulas for continuous compounding and monthly compounding. First, let's find the future value of Brandon's investment which is compounded continuously. Using the continuous compounding formula A = Pert, where P is the principal amount, e is Euler's number (approximately 2.71828), r is the annual interest rate as a decimal, and t is the time in years, the formula becomes A = 1100e(0.0775*18).
For Julian's investment compounding monthly, the formula is A = P(1 + r/n)nt, where n is the number of times interest is compounded per year. Plugging in the values gives us A = 1100(1 + 0.0825/12)12*18. After calculating both, we then subtract the future value of Brandon's investment from Julian's to find out the difference.
As demonstrated in the examples provided, the impact of compound interest on investments is significant over time, especially with different compounding frequencies and rates. Therefore, while we've not computed the exact figure here, Julian is likely to have more money than Brandon due to a higher interest rate compounded more frequently.