Suppose that you make deposits of $500 at the beginning of every year into an Individual Retirement Account (IRA) earning interest r. At the beginning of the first year, the value of the account will be $500; at the beginning of the second year, the value of the account, will be

(a) Verify that the value of the account at the beginning of the third year is T(r) = 500r² + 1500r + 1500.

(b) The account value at the beginning of the fourth year is F(r) = 500r³ + 2000r² + 3000r + 2000. If the annual rate of interest is 5% = 0.05, what will be the value of the account at the beginning of the fourth year?

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$500 = $500(1+r) + $500 = 500r + 1000 Value of 2nd deposit $500 + $500r Value of 1st deposlt