The Continental Bank advertises capital savings at 5.3% compounded annually while TD Canada Trust offers premium savings at 5.05% compounded monthly. Suppose you have $1000 to invest for two years.
(a) Which deposit will earn more interest?
(b) What is the difference in the amount of interest?
(a) The (Continental Bank/ TD Canada Bank) savings account will earn more interest
(b) The difference is $
(Round the final answer to the nearest cent as needed. Round all intermediate values to six decimal places as needed.)

Step 1 ：Given that the present value (PV) is $1000, the annual interest rate for Continental Bank (r_cont) is 5.3% or 0.053, the annual interest rate for TD Canada Trust (r_td) is 5.05% or 0.0505, the number of times that interest is compounded per year for Continental Bank (n_cont) is 1, the number of times that interest is compounded per year for TD Canada Trust (n_td) is 12, and the number of years the money is invested for (t) is 2.

Step 2 ：We can calculate the future value (FV) for both banks using the formula: \(FV = PV * (1 + r/n)^(nt)\).

Step 3 ：For Continental Bank, the future value (FV_cont) is calculated as: \(FV_{cont} = 1000 * (1 + 0.053/1)^(1*2) = 1108.809\).

Step 4 ：For TD Canada Trust, the future value (FV_td) is calculated as: \(FV_{td} = 1000 * (1 + 0.0505/12)^(12*2) = 1106.0422173012605\).

Step 5 ：We can then subtract the initial investment to find the interest earned for both banks. For Continental Bank, the interest earned (interest_cont) is: \(interest_{cont} = 1108.809 - 1000 = 108.80899999999997\). For TD Canada Trust, the interest earned (interest_td) is: \(interest_{td} = 1106.0422173012605 - 1000 = 106.04221730126051\).

Step 6 ：The bank with the higher interest earned is the one that will earn more interest. In this case, the Continental Bank savings account will earn more interest.

Step 7 ：The difference in the amount of interest (diff_interest) is simply the difference between the two interest amounts: \(diff_{interest} = 108.80899999999997 - 106.04221730126051 = 2.766782698739462\).

Step 8 ：Final Answer: \(\boxed{(a)\ The\ Continental\ Bank\ savings\ account\ will\ earn\ more\ interest.\ (b)\ The\ difference\ is\ \$2.77.}\)