A woman deposits $10,000 at the end of each year for 11 years in an investment account with a guaranteed interest rate of 7% compounded annually. (a) Find the value in the account at the end of the 11 years. (b) Her sister works for an investment firm that pays 6% 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 11 years? (c) How much would she lose or gain over 11 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 should be used. The value in the account at the end of the 11 years will be $ (Do not round until the final answer. Then round to the nearest cent as needed.) (b) She will have a total of $ in her account at her sister's firm at the end of 11 years. (Do not round until the final answer. Then round to the nearest cent as needed.) (c) She would $ over 11 years by investing in her sister's firm. (Do not round until the final answer. Then round to the nearest cent as needed.)