Pat and Sam own their own business, and have an automatic account builder set up with an investment company. At the end of each quarter, the company automatically deducts $2000 from their business checking account and puts it into a savings account, which they have set up for their children's college tuition. The account earns 4.8% annual interest compounded quarterly.

(Please show and explain work)

a. Write the bucket method expression for the account balance after 18 years. Use ... if you wish to skip some of the terms but be sure that you know what the exponent for the first and last terms should be and why!

b. How much would the first $2000 deposit (just the first deposit) ultimately contribute to the amount in account at the end of 18 years? [This is a regular compound interest problem, since it pertains to just one deposit.]

c. How much will be in the account, in total, after 18 years? [This is an annuity problem, since it pertains to many deposits accumulating to a large sum in the end.] d. How much of the account value after 18 years will be interest earned? Use your calculation from part c to help you.