A woman deposits $13,000 at the end of each year for 12 years in an investment account with a guaranteed interest rate of 4% compounded annually. (a) Find the value in the account at the end of the 12 years. (b) Her sister works for an investment firm that pays 3% compounded annually. If the woman deposits money with this firm instead of the one in part (a), how much will she have in her account at the end of 12 years? (c) How much would she lose or gain over 12 years by investing in her sister's firm? (a) The woman's deposits form an because the deposits are made at the of each period. Therefore, the formula FV=PMT[i(1+i)n1] should be used. The value in the account at the end of the 12 years will be $ (Do not round until the final answer. Then round to the nearest cent as needed.)