Lily wants to open an investment account to save for a down payment on a house. The growth of the account that her banker recommends (account A) can be modeled by the function A(t) = 3,000(1.024)4t, where t is the number of years that the account is open. She is also considering some other account options at different banks. Those accounts are modeled using the following functions:
Account B: B(t) = 3,000(1.008)12t
Account C: C(t) = 3,000(1.032)2t

Part A
If Lily chooses account A, the balance of her account would increase by a rate of 2.4% on a quarterly basis.

Part B
Lily manipulated the function representing account B in order to compare the rates of accounts A and B. Her work is shown here:
B(t) = 3,000(1.008)^12t
B(t) = 3,000(1.008)^4(12/3 * t)
B(t) = 3,000(1.008)^4 * 4t
B(t) ≈ 3,000(1.0324)^4t

Which statement is true?
a. Lily should have multiplied 1.008 by 4 instead of raising 1.008 to the power of 4.
b. Lily didn’t make any mistakes.
c. Lily should have divided 12 by 4 instead of 3.
d. Lily should have raised 1.008 to the power of 3 instead of 4.

Part C
Consider the function representing account C. Rewrite the function to reveal the quarterly interest rate on the account. Round the base of the exponential expression to four places, if necessary.

Enter the correct answer in the box.
C(t) = 3000(1.032)^2t

Part D
Which account would you recommend to Lily? Justify your answer in two to three sentences.