Final answer:
The question involves comparing the future values of two investments using distinct compounding methods - quarterly and continuous - to determine which would yield a higher return after 9 years. Using specific formulas for each method, we calculate the future value for both investments and then find the difference to see how much more money Myesha would have compared to Magan.
Step-by-step explanation:
The question asks to compare the future value of two investments, one with quarterly compounding interest and the other with continuous compounding interest, both over a period of 9 years with the same principal amount of $210.
For the quarterly compounding interest, we use the formula A = P(1 + r/n)^(nt), where A is the amount of money accumulated after n years, P is the principal amount, r is the annual interest rate, n is the number of times that interest is compounded per year, and t is the time the money is invested for in years.
For Magan's investment:
A = 210(1 + 0.095/4)^(4*9) to get the future value.
For the continuous compounding interest, we use the formula A = Pe^(rt), where A is the amount, P is the principal amount, e is Euler's number (approx. 2.71828), r is the annual interest rate, and t is the time in years.
For Myesha's investment:
A = 210e^(0.0975*9) to get the future value.
Subtract Magan's future value from Myesha's future value and round to the nearest dollar to determine how much more money Myesha would have in her account after 9 years compared to Magan.