Suppose that 55 comma 00055,000 is invested at 3 and one half3 1 2% interest, compounded quarterly. a) Find the function for the amount to which the investment grows after t years. b) Find the amount of money in the account at tequals=00, 44, 77, and 10 years.

(a)

(b) At t = 0, A = 55,000

At t = 4, A = 58,162.19

At t = 7, A = 60,652.57

At t = 10, A = 63,249.60

Step-by-step explanation:

(a) The amount on a compound interest is given by

P is the principal invested, R is the rate and T is the time.

The principal is 55,000. With the interest compounded quarterly, there are four compundings in a year. Hence each year will have four periods.

The function for the amount is then

(b)

At t = 0,

At t = 4,

At t = 7,

At t = 10,