Juanita and Toñita are going to invest $200,000; In 3 years, different institutions offer them an interest rate of 8%, with which bank should they invest if the capitalization: a) in BBW is monthly b) in CHSC it is biweekly c) BX is continuous.

This is a question about comparing different types of interest capitalization. Interest capitalization is the process of adding the interest accrued on a loan or an investment to the principal amount, so that the interest earns interest in the future. There are different ways of capitalizing interest, depending on how frequently the interest is calculated and added to the principal. Some common types of interest capitalization are monthly, biweekly, and continuous. To compare the different types of interest capitalization, we need to use the following formula to calculate the future value of an investment after a certain period of time: $$FV = PV(1 + r)^n$$ where, - FV is the future value of the investment - PV is the present value or the initial amount of the investment - r is the interest rate per period - n is the number of periods In this question, we are given the following information: - The present value or the initial amount of the investment is $200,000 - The interest rate is 8% per year - The number of years is 3 - We want to compare the future value of the investment if the capitalization is monthly, biweekly, or continuous Using this information, we can calculate the future value of the investment for each type of capitalization as follows: - Monthly capitalization: This means that the interest is calculated and added to the principal every month. Therefore, the number of periods is 12 times the number of years, and the interest rate per period is one-twelfth of the annual interest rate. We can plug in these values into the formula and get: $$FV = 200000(1 + 0.08/12)^{12 \times 3}$$ $$FV \approx 254,047.41$$ - Biweekly capitalization: This means that the interest is calculated and added to the principal every two weeks. Therefore, the number of periods is 26 times the number of years, and the interest rate per period is one-twenty-sixth of the annual interest rate. We can plug in these values into the formula and get: $$FV = 200000(1 + 0.08/26)^{26 \times 3}$$ $$FV \approx 254,156.16$$ - Continuous capitalization: This means that the interest is calculated and added to the principal continuously. Therefore, there is no fixed number of periods or interest rate per period. Instead, we use a different formula that involves a natural exponential function: $$FV = PVe^{rt}$$ where, - e is a mathematical constant that is approximately equal to 2.71828 - t is the time in years We can plug in these values into the formula and get: $$FV = 200000e^{0.08 \times 3}$$ $$FV \approx 254,249.83$$ Therefore, Juanita and Toñita should invest with BX, because it offers continuous capitalization, which results in the highest future value of their investment after three years.