Final answer:
The problem asks for the difference in future values of two investments with different compounding periods and interest rates after 18 years. To solve it, we apply the appropriate compound interest formulas for continuous and monthly compounding to Brandon's and Julian's accounts, respectively, and then find the difference between the two amounts, rounding to the nearest dollar.
Step-by-step explanation:
The question involves calculating the future value of investments with compound interest, which varies by the compounding frequency and interest rate. The compound interest formula varies depending on whether the compounding is continuous or periodic. In the case of continuous compounding, the formula is A = Pert, where A is the amount of money accumulated after n years, including interest, P is the principal amount, r is the interest rate, and t is the time in years. For periodic compounding, the formula is A = P(1 + r/n)nt, where n is the number of times that interest is compounded per year.
For Brandon, with continuous compounding at a rate of 7.75%, the formula would be A = 1100e0.0775*18.
For Julian, with monthly compounding at a rate of 8.25%, we calculate the future value using A = 1100(1 + 0.0825/12)12*18.
To find out how much more money Julian would have in his account than Brandon after 18 years, we subtract the future value of Brandon's account from Julian's and round to the nearest dollar.