The Continental Bank advertises capital savings at $6.9 \%$ compounded annually while TD Canada Trust offers premium savings at $6.83 \%$ compounded quarterly. Suppose you have $\$ 2500$ to invest for two years. (a) Which deposit will eam more interest? (b) What is the difference in the amount of interest? (a) The 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 initial investment (PV) is $2500, the annual interest rate for the Continental Bank (r_cont) is 6.9%, the annual interest rate for TD Canada Trust (r_td) is 6.83%, the number of times that interest is compounded per year for the Continental Bank (n_cont) is 1, the number of times that interest is compounded per year for TD Canada Trust (n_td) is 4, and the number of years the money is invested for (t) is 2.

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

Step 3 ：For the Continental Bank, \(FV_{cont} = 2500 * (1 + 0.069/1)^{1*2} = 2856.9024999999997\).

Step 4 ：For TD Canada Trust, \(FV_{td} = 2500 * (1 + 0.0683/4)^{4*2} = 2862.6209382380202\).

Step 5 ：Subtract the initial investment from the future value to find the interest earned for both banks.

Step 6 ：For the Continental Bank, the interest earned is \(interest_{cont} = 2856.9024999999997 - 2500 = 356.9024999999997\).

Step 7 ：For TD Canada Trust, the interest earned is \(interest_{td} = 2862.6209382380202 - 2500 = 362.62093823802024\).

Step 8 ：TD Canada Trust earns more interest, so it is the better investment.

Step 9 ：Calculate the difference in the amount of interest between the two banks: \(interest_{diff} = 362.62093823802024 - 356.9024999999997 = 5.718438238020553\).

Step 10 ：\(\boxed{\text{(a) TD Canada Trust}}\)

Step 11 ：\(\boxed{\text{(b) $5.72}}\)